Draw a sphere
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Draw a sphere.
The sphere can be represented graphically, or in ASCII art, depending on the language capabilities.
Either static or rotational projection is acceptable for this task.
- Related tasks
11l
V shades = [‘.’, ‘:’, ‘!’, ‘*’, ‘o’, ‘e’, ‘&’, ‘#’, ‘%’, ‘@’]
F dotp(v1, v2)
V d = dot(v1, v2)
R I d < 0 {-d} E 0.0
F draw_sphere(r, k, ambient, light)
L(i) Int(floor(-r)) .< Int(ceil(r) + 1)
V x = i + 0.5
V line = ‘’
L(j) Int(floor(-2 * r)) .< Int(ceil(2 * r) + 1)
V y = j / 2 + 0.5
I x * x + y * y <= r * r
V vec = normalize((x, y, sqrt(r * r - x * x - y * y)))
V b = dotp(light, vec) ^ k + ambient
V intensity = Int((1 - b) * (:shades.len - 1))
line ‘’= I intensity C 0 .< :shades.len {:shades[intensity]} E :shades[0]
E
line ‘’= ‘ ’
print(line)
V light = normalize((30.0, 30.0, -50.0))
draw_sphere(20, 4, 0.1, light)
draw_sphere(10, 2, 0.4, light)- Output:
&&&&&&&&&&#######
&eeeeeeeeeeeeeeee&&&&&&#######%
&eoooo*******oooooooeeeee&&&&&########%
eoo****!!!!!!!!******oooooeeee&&&&&########%%
eoo**!!!!::::::::!!!!!*****ooooeeee&&&&&########%%%
eo**!!::::::...:::::::!!!!!***ooooeeee&&&&&########%%%%
eo*!!:::.............:::::!!!!***ooooeeee&&&&&########%%%%%
eo*!!:::.................::::!!!!***ooooeeee&&&&#########%%%%%%
eo*!!::....................::::!!!****oooeeee&&&&&#########%%%%%%
&o**!::......................::::!!!****oooeeee&&&&&##########%%%%%%%
&o**!::.......................::::!!!****oooeeee&&&&&##########%%%%%%%%
&oo*!!::.......................:::!!!!***ooooeeee&&&&&##########%%%%%%%%%
&eo*!!::.......................::::!!!****ooooeeee&&&&&##########%%%%%%%%%%
eo**!!::......................::::!!!!***ooooeeeee&&&&&##########%%%%%%%%%%
&eo**!!:::...................:::::!!!!****ooooeeee&&&&&###########%%%%%%%%%%%
eeo**!!::::................:::::!!!!!****ooooeeee&&&&&&###########%%%%%%%%%%%
&eeo***!!:::::...........::::::!!!!!****oooooeeee&&&&&&###########%%%%%%%%%%%%%
&eeoo**!!!!::::::::::::::::::!!!!!*****ooooeeeee&&&&&&############%%%%%%%%%%%%%
&eeooo***!!!!::::::::::::!!!!!!!*****oooooeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeooo***!!!!!!!!!!!!!!!!!!!******oooooeeeeee&&&&&&############%%%%%%%%%%%%%%%
&&eeeooo******!!!!!!!!!!********ooooooeeeeee&&&&&&&############%%%%%%%%%%%%%%%%
#&&eeeooooo******************oooooooeeeeee&&&&&&&#############%%%%%%%%%%%%%%%%%
#&&&eeeeoooooooo******oooooooooooeeeeeee&&&&&&&&#############%%%%%%%%%%%%%%%%%%
##&&&&eeeeeooooooooooooooooooeeeeeeee&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%
##&&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&################%%%%%%%%%%%%%%%%%%%
####&&&&&&eeeeeeeeeeeeeeeeeee&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%%
#####&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#################%%%%%%%%%%%%%%%%%%%%%%
%#######&&&&&&&&&&&&&&&&&&&&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%
%###########&&&&&&&&&&&&&#######################%%%%%%%%%%%%%%%%%%%%%%%%%
%############################################%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%#########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%#############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::...:::!!!*o
..............::!!*oo
..................::!!**ooe
.....................::!!**ooee
.......................::!!**ooee
........................::!!**oooee
.........................::!!**oooeee
:........................::!!!**oooeeee
........................::!!!**ooooeeee
:......................::!!!***oooeeeee
:....................:::!!!***oooeeeeee
!:.................:::!!!****oooeeeeeee
*!:::...........::::!!!!***ooooeeeeeeee
*!!!:::::::::::!!!!!****oooooeeeeeeee
o**!!!!!!!!!!!!!*****oooooeeeeeeeee
oo**************ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
Action!
INT ARRAY SinTab=[
0 4 9 13 18 22 27 31 36 40 44 49 53 58 62 66 71 75 79 83
88 92 96 100 104 108 112 116 120 124 128 132 136 139 143
147 150 154 158 161 165 168 171 175 178 181 184 187 190
193 196 199 202 204 207 210 212 215 217 219 222 224 226
228 230 232 234 236 237 239 241 242 243 245 246 247 248
249 250 251 252 253 254 254 255 255 255 256 256 256 256]
INT FUNC Sin(INT a)
WHILE a<0 DO a==+360 OD
WHILE a>360 DO a==-360 OD
IF a<=90 THEN
RETURN (SinTab(a))
ELSEIF a<=180 THEN
RETURN (SinTab(180-a))
ELSEIF a<=270 THEN
RETURN (-SinTab(a-180))
ELSE
RETURN (-SinTab(360-a))
FI
RETURN (0)
INT FUNC Cos(INT a)
RETURN (Sin(a-90))
PROC Ellipse(INT x0,y0,rx,ry)
INT i
CARD x
BYTE y
x=x0+rx*Sin(0)/256
y=y0+ry*Cos(0)/256
Plot(x,y)
FOR i=5 TO 360 STEP 5
DO
x=x0+rx*Sin(i)/256
y=y0+ry*Cos(i)/256
DrawTo(x,y)
OD
RETURN
PROC Main()
BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6
INT cx=[160],cy=[96],r=[90],r2
BYTE i
Graphics(8+16)
COLOR1=$0C
COLOR2=$02
Color=1
Ellipse(cx,cy,r,r)
FOR i=10 TO 90 STEP 10
DO
r2=r*Cos(i)/256
Ellipse(cx,cy,r,r2)
Ellipse(cx,cy,r2,r)
OD
DO UNTIL CH#$FF OD
CH=$FF
RETURN- Output:
Screenshot from Atari 8-bit computer
Ada
Translation from the C code at http://cairographics.org/samples/gradient Uses the Cairo component of GtkAda to create and save as png
with Glib; use Glib;
with Cairo; use Cairo;
with Cairo.Png; use Cairo.Png;
with Cairo.Pattern; use Cairo.Pattern;
with Cairo.Image_Surface; use Cairo.Image_Surface;
with Ada.Numerics;
procedure Sphere is
subtype Dub is Glib.Gdouble;
Surface : Cairo_Surface;
Cr : Cairo_Context;
Pat : Cairo_Pattern;
Status_Out : Cairo_Status;
M_Pi : constant Dub := Dub (Ada.Numerics.Pi);
begin
Surface := Create (Cairo_Format_ARGB32, 512, 512);
Cr := Create (Surface);
Pat :=
Cairo.Pattern.Create_Radial (230.4, 204.8, 51.1, 204.8, 204.8, 256.0);
Cairo.Pattern.Add_Color_Stop_Rgba (Pat, 0.0, 1.0, 1.0, 1.0, 1.0);
Cairo.Pattern.Add_Color_Stop_Rgba (Pat, 1.0, 0.0, 0.0, 0.0, 1.0);
Cairo.Set_Source (Cr, Pat);
Cairo.Arc (Cr, 256.0, 256.0, 153.6, 0.0, 2.0 * M_Pi);
Cairo.Fill (Cr);
Cairo.Pattern.Destroy (Pat);
Status_Out := Write_To_Png (Surface, "SphereAda.png");
pragma Assert (Status_Out = Cairo_Status_Success);
end Sphere;
This uses a very loose binding to SDL as found in any GPS installation. For it to work, you must choose New Project From Templte|Empty Game
with Display; use Display;
with Display.Basic; use Display.Basic;
procedure Main is
Ball : Shape_Id := New_Circle
(X => 0.0,
Y => 0.0,
Radius => 20.0,
Color => Blue);
begin
null;
end Main;
ALGOL W
with some changes inspired by other samples.
begin
% draw a sphere %
% returns the next integer larger than x or x if x is an integer %
integer procedure ceil( real value x ) ;
begin
integer tmp;
tmp := truncate( x );
if tmp not = x then tmp + 1 else tmp
end ciel ;
% returns the absolute value of the dot product of x and y or 0 if it is not negative %
real procedure dot( real array x, y ( * ) ) ;
begin
real tmp;
tmp := x( 1 ) * y( 1 ) + x( 2 ) * y( 2 ) + x( 3 ) * y( 3 );
if tmp < 0 then - tmp else 0
end dot ;
% normalises the vector v %
procedure normalize( real array v ( * ) ) ;
begin
real tmp;
tmp := sqrt( v( 1 ) * v( 1 ) + v( 2 ) * v( 2 ) + v( 3 ) * v( 3 ) );
for i := 1 until 3 do v( i ) := v( i ) / tmp
end normalize ;
% draws a sphere using ASCII art %
procedure drawSphere( real value radius
; integer value k
; real value ambient
; real array light ( * )
; string(10) value shades
) ;
begin
real array vec ( 1 :: 3 );
integer intensity, maxShades;
real diameter, r2;
maxShades := 9;
diameter := 2 * radius;
r2 := radius * radius;
for i := entier( - radius ) until ceil( radius ) do begin
real x, x2;
integer linePos;
string(256) line;
linePos := 0;
x := i + 0.5;
x2 := x * x;
line := "";
for j := entier( - diameter ) until ceil( diameter ) do begin
real y, y2;
y := j / 2 + 0.5;
y2 := y * y;
if x2 + y2 <= r2 then begin
real b, dp;
vec( 1 ) := x;
vec( 2 ) := y;
vec( 3 ) := sqrt( r2 - x2 - y2 );
normalize( vec );
dp := dot( light, vec );
b := dp;
for p := 2 until k do b := b * dp;
b := b + ambient;
intensity := round( ( 1 - b ) * maxShades );
if intensity < 0 then intensity := 0;
if intensity > maxShades then intensity := maxShades;
line( linePos // 1 ) := shades( intensity // 1 );
end
else line( linePos // 1 ) := " "
;
if linePos < 255 then linePos := linePos + 1
end for_j ;
write( s_w := 0, line( 0 // 1 ) );
for c := 1 until if linePos > 255 then 255 else linePos - 1 do writeon( s_w := 0, line( c // 1 ) )
end for_i
end drawSphere ;
% test drawSphere %
begin
real array light ( 1 :: 3 );
integer maxShades;
light( 1 ) := 30;
light( 2 ) := 30;
light( 3 ) := -59;
normalize( light );
drawSphere( 20, 4, 0.1, light, ".:!*oe#%&@" );
drawSphere( 10, 2, 0.4, light, ".:!*oe#%&@" )
end test
end.- Output:
%%%%%%%%%%%%%&&&&
%%#################%%%%%%%&&&&&
%##eeeeeooooooeeeeeee######%%%%%%&&&&&&
##eeooooo*******oooooooeeeee####%%%%%%&&&&&&&
##eooo*****!!!!!!!******oooooeeee####%%%%%%&&&&&&&&
#eeoo**!!!!!!!:::!!!!!!!*****ooooeeee####%%%%%&&&&&&&&&
#eoo**!!!:::::::::::::::!!!!****ooooeeee####%%%%%%&&&&&&&&&
#eeo**!!!::::.........::::::!!!!***ooooeeee####%%%%%%&&&&&&&&&&
#eoo*!!!:::..............:::::!!!!***ooooeee#####%%%%%&&&&&&&&&&&
%#eo**!!:::..................::::!!!****oooeeee####%%%%%%&&&&&&&&&&&&
%#eo**!!:::...................::::!!!!***oooeeee####%%%%%%&&&&&&&&&&&&&
%#eo**!!:::....................::::!!!!***oooeeee####%%%%%%&&&&&&&&&&&&&&
%#eoo**!!::.....................::::!!!****oooeeee####%%%%%%&&&&&&&&&&&&&&&
#eeo**!!:::....................::::!!!!***ooooeeee####%%%%%%&&&&&&&&&&&&&&&
%#eoo**!!::::..................::::!!!!****oooeeee#####%%%%%%&&&&&&&&&&&&&&&&
##eoo**!!!::::...............:::::!!!!****ooooeeee####%%%%%%%&&&&&&&&&&&&&&&&
%##eoo***!!!:::::..........::::::!!!!!****ooooeeee#####%%%%%%%&&&&&&&&&&&&&&&&&
%##eeoo**!!!!::::::::::::::::::!!!!!*****ooooeeee#####%%%%%%%&&&&&&&&&&&&&&&&&&
%##eeooo***!!!!!::::::::::::!!!!!!*****ooooeeeee#####%%%%%%%&&&&&&&&&&&&&&&&&&&
%##eeeooo****!!!!!!!!!!!!!!!!!!******oooooeeeee#####%%%%%%%&&&&&&&&&&&&&&&&&&&&
%%##eeeooo******!!!!!!!!!!!********oooooeeeee######%%%%%%%&&&&&&&&&&&&&&&&&&&&&
%%###eeeooooo******************oooooooeeeeee######%%%%%%%&&&&&&&&&&&&&&&&&&&&&&
&%%###eeeeooooooo*********oooooooooeeeeee#######%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&
&%%%####eeeeeooooooooooooooooooeeeeeeee#######%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&
&%%%%####eeeeeeeeeeeeeeeeeeeeeeeeee########%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&
&&%%%%#######eeeeeeeeeeeeeeeee##########%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&%%%%%%############################%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&%%%%%%%#####################%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
!!::::!!!**oo
:...........:::!!**oe
:.................::!!*ooee
:....................::!!**ooee
......................::!!**ooeee
........................::!!**ooeee
:........................::!!**ooeeee
!........................::!!!**ooeeeee
:.......................:::!!**oooeeeee
:......................:::!!***ooeeeeee
!:....................:::!!***oooeeeeee
*!:.................:::!!!***oooeeeeeee
o*!:::..........:::::!!!***ooooeeeeeeee
o*!!!:::::::::::!!!!!***ooooeeeeeeeee
o***!!!!!!!!!!!!*****ooooeeeeeeeeee
eoo*************ooooooeeeeeeeeeee
eeoooooooooooooooeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
Arendelle
[ #j ,
[ #i ,
{ ( #x - 19 ) ^ 2 +
( #y - 14 ) ^ 2 < 125 , p
} r
] [ #i , l ] d
]
ATS
(*
** Solution to Draw_a_sphere.dats
*)
(* ****** ****** *)
//
#include
"share/atspre_define.hats" // defines some names
#include
"share/atspre_staload.hats" // for targeting C
#include
"share/HATS/atspre_staload_libats_ML.hats" // for ...
#include
"share/HATS/atslib_staload_libats_libc.hats" // for libc
//
(* ****** ****** *)
extern
fun
Draw_a_sphere
(
R: double, k: double, ambient: double
) : void // end of [Draw_a_sphere]
(* ****** ****** *)
implement
Draw_a_sphere
(
R: double, k: double, ambient: double
) = let
fun normalize(v0: double, v1: double, v2: double): (double, double, double) = let
val len = sqrt(v0*v0+v1*v1+v2*v2)
in
(v0/len, v1/len, v2/len)
end // end of [normalize]
fun dot(v0: double, v1: double, v2: double, x0: double, x1: double, x2: double): double = let
val d = v0*x0+v1*x1+v2*x2
val sgn = gcompare_val_val<double> (d, 0.0)
in
if sgn < 0 then ~d else 0.0
end // end of [dot]
fun print_char(i: int): void =
if i = 0 then print!(".") else
if i = 1 then print!(":") else
if i = 2 then print!("!") else
if i = 3 then print!("*") else
if i = 4 then print!("o") else
if i = 5 then print!("e") else
if i = 6 then print!("&") else
if i = 7 then print!("#") else
if i = 8 then print!("%") else
if i = 9 then print!("@") else print!(" ")
val i_start = floor(~R)
val i_end = ceil(R)
val j_start = floor(~2 * R)
val j_end = ceil(2 * R)
val (l0, l1, l2) = normalize(30.0, 30.0, ~50.0)
fun loopj(j: int, j_end: int, x: double): void = let
val y = j / 2.0 + 0.5;
val sgn = gcompare_val_val<double> (x*x + y*y, R*R)
val (v0, v1, v2) = normalize(x, y, sqrt(R*R - x*x - y*y))
val b = pow(dot(l0, l1, l2, v0, v1, v2), k) + ambient
val intensity = 9.0 - 9.0*b
val sgn2 = gcompare_val_val<double> (intensity, 0.0)
val sgn3 = gcompare_val_val<double> (intensity, 9.0)
in
( if sgn > 0 then print_char(10) else
if sgn2 < 0 then print_char(0) else
if sgn3 >= 0 then print_char(8) else
print_char(g0float2int(intensity));
if j < j_end then loopj(j+1, j_end, x)
)
end // end of [loopj]
fun loopi(i: int, i_end: int, j: int, j_end: int): void = let
val x = i + 0.5
val () = loopj(j, j_end, x)
val () = println!()
in
if i < i_end then loopi(i+1, i_end, j, j_end)
end // end of [loopi]
in
loopi(g0float2int(i_start), g0float2int(i_end), g0float2int(j_start), g0float2int(j_end))
end
(* ****** ****** *)
implement
main0() = () where
{
val () = DrawSphere(20.0, 4.0, .1)
val () = DrawSphere(10.0, 2.0, .4)
} (* end of [main0] *)
(* ****** ****** *)
AutoHotkey
#NoEnv
SetBatchLines, -1
#SingleInstance, Force
; Uncomment if Gdip.ahk is not in your standard library
#Include, Gdip.ahk
; Settings
X := 200, Y := 200, Width := 200, Height := 200 ; Location and size of sphere
rotation := -30 ; degrees
ARGB := 0xFFFF0000 ; Color=Solid Red
If !pToken := Gdip_Startup() ; Start gdi+
{
MsgBox, 48, gdiplus error!, Gdiplus failed to start. Please ensure you have gdiplus on your system
ExitApp
}
OnExit, Exit
Gui, -Caption +E0x80000 +LastFound +AlwaysOnTop +ToolWindow +OwnDialogs ; Create GUI
Gui, Show, NA ; Show GUI
hwnd1 := WinExist() ; Get a handle to this window we have created in order to update it later
hbm := CreateDIBSection(A_ScreenWidth, A_ScreenHeight) ; Create a gdi bitmap drawing area
hdc := CreateCompatibleDC() ; Get a device context compatible with the screen
obm := SelectObject(hdc, hbm) ; Select the bitmap into the device context
pGraphics := Gdip_GraphicsFromHDC(hdc) ; Get a pointer to the graphics of the bitmap, for use with drawing functions
Gdip_SetSmoothingMode(pGraphics, 4) ; Set the smoothing mode to antialias = 4 to make shapes appear smother
Gdip_TranslateWorldTransform(pGraphics, X, Y)
Gdip_RotateWorldTransform(pGraphics, rotation)
; Base ellipse
pBrush := Gdip_CreateLineBrushFromRect(0, 0, Width, Height, ARGB, 0xFF000000)
Gdip_FillEllipse(pGraphics, pBrush, 0, 0, Width, Height)
; First highlight ellipse
pBrush := Gdip_CreateLineBrushFromRect(Width*0.1, Height*0.01, Width*0.8, Height*0.6, 0x33FFFFFF, 0x00FFFFFF)
Gdip_FillEllipse(pGraphics, pBrush, Width*0.1, Height*0.01, Width*0.8, Height*0.6)
; Second highlight ellipse
pBrush := Gdip_CreateLineBrushFromRect(Width*0.3, Height*0.02, Width*0.3, Height*0.2, 0xBBFFFFFF, 0x00FFFFFF)
Gdip_FillEllipse(pGraphics, pBrush, Width*0.3, Height*0.02, Width*0.3, Height*0.2)
UpdateLayeredWindow(hwnd1, hdc, 0, 0, A_ScreenWidth, A_ScreenHeight)
SelectObject(hdc, obm) ; Select the object back into the hdc
Gdip_DeletePath(Path)
Gdip_DeleteBrush(pBrush)
DeleteObject(hbm) ; Now the bitmap may be deleted
DeleteDC(hdc) ; Also the device context related to the bitmap may be deleted
Gdip_DeleteGraphics(G) ; The graphics may now be deleted
Return
Exit:
; gdi+ may now be shutdown on exiting the program
Gdip_Shutdown(pToken)
ExitApp
AWK
# syntax: GAWK -f DRAW_A_SPHERE.AWK
# converted from VBSCRIPT
BEGIN {
draw_sphere(20,4,0.1)
draw_sphere(10,2,0.4)
exit(0)
}
function draw_sphere(radius,k,ambient, b,i,intensity,j,leng_shades,light,line,shades,vec,x,y) {
leng_shades = split0(".:!*oe&#%@",shades,"")
split("30,30,-50",light,",")
normalize(light)
for (i=int(-radius); i<=ceil(radius); i++) {
x = i + 0.5
line = ""
for (j=int(-2*radius); j<=ceil(2*radius); j++) {
y = j / 2 + 0.5
if (x*x + y*y <= radius*radius) {
vec[1] = x
vec[2] = y
vec[3] = sqrt(radius*radius - x*x - y*y)
normalize(vec)
b = dot(light,vec) ^ k + ambient
intensity = int((1-b) * leng_shades)
if (intensity < 0) {
intensity = 0
}
if (intensity >= leng_shades) {
intensity = leng_shades
}
line = line shades[intensity]
}
else {
line = line " "
}
}
printf("%s\n",line)
}
}
function ceil(x, tmp) {
tmp = int(x)
return (tmp != x) ? tmp+1 : tmp
}
function dot(x,y, tmp) {
tmp = x[1]*y[1] + x[2]*y[2] + x[3]*y[3]
return (tmp < 0) ? -tmp : 0
}
function normalize(v, tmp) {
tmp = sqrt(v[1]*v[1] + v[2]*v[2] + v[3]*v[3])
v[1] /= tmp
v[2] /= tmp
v[3] /= tmp
}
function split0(str,array,fs, arr,i,n) { # same as split except indices start at zero
n = split(str,arr,fs)
for (i=1; i<=n; i++) {
array[i-1] = arr[i]
}
return(n)
}
- Output:
############%%%%%
#&&&eeeeeeeee&&&&&&#####%%%%%%%
&eeeoooooooooooooeeeee&&&&#####%%%%%%%%
&eoo***************oooooeeee&&&&####%%%%%%%%%
&eo***!!!!!:::!!!!!!!****ooooeee&&&&#####%%%%%%%%%%
eoo*!!!::::::::::::::!!!!****oooeeee&&&#####%%%%%%%%%%%
eo**!!:::............::::!!!!***oooeeee&&&#####%%%%%%%%%%%%
&eo*!!::.................:::!!!!***oooeee&&&&#####%%%%%%%%%%%%%
eo*!!::...................::::!!!***oooeeee&&&#####%%%%%%%%%%%%%%
#eo*!!::.....................:::!!!***oooeeee&&&&####%%%%%%%%%%%%%%%@
&eo*!!::......................:::!!!***oooeeee&&&&#####%%%%%%%%%%%%%%%@
&eo*!!::......................::::!!!***oooeeee&&&&#####%%%%%%%%%%%%%%%@@
#eo**!!::......................:::!!!****oooeee&&&&#####%%%%%%%%%%%%%%%%%@@
&eo**!:::....................::::!!!!***oooeeee&&&&#####%%%%%%%%%%%%%%%%%@@
&eoo**!!::...................::::!!!!***ooooeee&&&&######%%%%%%%%%%%%%%%%%@@@
&eoo**!!:::................::::!!!!****ooooeee&&&&&#####%%%%%%%%%%%%%%%%%%@@@
#&eoo**!!!::::...........:::::!!!!!****oooeeee&&&&&######%%%%%%%%%%%%%%%%%%@@@@
#&eeoo**!!!!::::::::::::::::!!!!!****ooooeeee&&&&&######%%%%%%%%%%%%%%%%%%%@@@@
#&eeooo***!!!!!::::::::!!!!!!!*****ooooeeeee&&&&&######%%%%%%%%%%%%%%%%%%%@@@@@
#&&eeooo****!!!!!!!!!!!!!!!******oooooeeee&&&&&#######%%%%%%%%%%%%%%%%%%%%@@@@@
##&&eeoooo********************oooooeeeee&&&&&&######%%%%%%%%%%%%%%%%%%%%%%@@@@@
##&&&eeeoooooo***********oooooooeeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%@@@@@@
%##&&&eeeeeooooooooooooooooooeeeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@
%%###&&&&eeeeeeeeeeoeeeeeeeeeeee&&&&&&&&########%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@
%%###&&&&&&eeeeeeeeeeeeeeee&&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@
%%%#####&&&&&&&&&&&&&&&&&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@
%%%%#######&&&&&&&&&&&&&&&############%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@
%%%%%%#############################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@
%%%%%%%%######################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@
%%%%%%%%%%%%%%%#####%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@@@
@%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@@@@
@@@@%%%%%%%%%%%%@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@
::..::::!!**o
.............::!!**oe
..................::!!*ooee
.....................::!!*ooeee
.......................:!!**ooeee
........................:!!**ooeeee
........................::!!**ooeeee&
:........................::!!**ooeeee&&
........................::!!**oooeeee&&
:......................::!!***ooeeeee&&
:....................::!!!***ooeeeee&&&
!::................:::!!***oooeeeeee&&&
*!!::..........::::!!!****oooeeeeee&&&&
**!!::::::::::!!!!!***ooooeeeeee&&&&&
o***!!!!!!!!!!*****ooooeeeeeee&&&&&
eooo*********ooooooeeeeeeee&&&&&&
eeeoooooooooooeeeeeeeeee&&&&&&&
eeeeeeeeeeeeeeeeeee&&&&&&&&
&eeeeeeeeee&&&&&&&&&&
&&&&&&&&&&&&&
BASIC
BASIC256
This is based, but not exactly, on the Tcl implementation. Thus, the output is almost the same to the output of Tcl implementation below.
clg
color white
rect 0,0,graphwidth, graphheight
for n = 1 to 100
color rgb(2*n,2*n,2*n)
circle 150-2*n/3,150-n/2,150-n
next nBBC BASIC
Using Direct3D.
MODE 8
INSTALL @lib$+"D3DLIB"
D3DTS_VIEW = 2
D3DTS_PROJECTION = 3
D3DRS_SPECULARENABLE = 29
SYS "LoadLibrary", @lib$+"D3DX8BBC.DLL" TO d3dx%
IF d3dx%=0 ERROR 100, "Couldn't load D3DX8BBC.DLL"
SYS "GetProcAddress", d3dx%, "D3DXCreateSphere" TO `D3DXCreateSphere`
SYS "GetProcAddress", d3dx%, "D3DXMatrixLookAtLH" TO `D3DXMatrixLookAtLH`
SYS "GetProcAddress", d3dx%, "D3DXMatrixPerspectiveFovLH" TO `D3DXMatrixPerspectiveFovLH`
DIM eyepos%(2), lookat%(2), up%(2), mat%(3,3)
DIM D3Dlight8{Type%, Diffuse{r%,g%,b%,a%}, Specular{r%,g%,b%,a%}, \
\ Ambient{r%,g%,b%,a%}, Position{x%,y%,z%}, Direction{x%,y%,z%}, \
\ Range%, Falloff%, Attenuation0%, Attenuation1%, Attenuation2%, \
\ Theta%, Phi%}
DIM D3Dmaterial8{Diffuse{r%,g%,b%,a%}, Ambient{r%,g%,b%,a%}, \
\ Specular{r%,g%,b%,a%}, Emissive{r%,g%,b%,a%}, Power%}
DIM D3Dbasemesh8{QueryInterface%, Addref%, Release%, \
\ DrawSubset%, GetNumFaces%, GetNumVertices%, GetFVF%, \
\ GetDeclaration%, GetOptions%, GetDevice%, \
\ CloneMeshFVF%, CloneMesh%, GetVertexBuffer%, GetIndexBuffer%, \
\ LockVertexBuffer%, UnlockVertexBuffer%, LockIndexBuffer%, \
\ UnlockIndexBuffer%, GetAttributeTable%}
DIM D3Ddevice8{QueryInterface%, AddRef%, Release%, TestCooperativeLevel%, \
\ GetAvailableTextureMem%, ResourceManagerDiscardBytes%, GetDirect3D%, \
\ GetDeviceCaps%, GetDisplayMode%, GetCreationParameters%, SetCursorProperties%, \
\ SetCursorPosition%, ShowCursor%, CreateAdditionalSwapChain%, Reset%, \
\ Present%, GetBackBuffer%, GetRasterStatus%, SetGammaRamp%, GetGammaRamp%, \
\ CreateTexture%, CreateVolumeTexture%, CreateCubeTexture%, CreateVertexBuffer%, \
\ CreateIndexBuffer%, CreateRenderTarget%, CreateDepthStencilSurface%, \
\ CreateImageSurface%, CopyRects%, UpdateTexture%, GetFrontBuffer%, \
\ SetRenderTarget%, GetRenderTarget%, GetDepthStencilSurface%, BeginScene%, \
\ EndScene%, Clear%, SetTransform%, GetTransform%, MultiplyTransform%, \
\ SetViewport%, GetViewport%, SetMaterial%, GetMaterial%, SetLight%, GetLight%, \
\ LightEnable%, GetLightEnable%, SetClipPlane%, GetClipPlane%, SetRenderState%, \
\ GetRenderState%, BeginStateBlock%, EndStateBlock%, ApplyStateBlock%, \
\ CaptureStateBlock%, DeleteStateBlock%, CreateStateBlock%, SetClipStatus%, \
\ GetClipStatus%, GetTexture%, SetTexture%, GetTextureStageState%, \
\ SetTextureStageState%, ValidateDevice%, GetInfo%, SetPaletteEntries%, \
\ GetPaletteEntries%, SetCurrentTexturePalette%, GetCurrentTexturePalette%, \
\ DrawPrimitive%, DrawIndexedPrimitive%, DrawPrimitiveUP%, \
\ DrawIndexedPrimitiveUP%, ProcessVertices%, CreateVertexShader%, \
\ SetVertexShader%, GetVertexShader%, DeleteVertexShader%, \
\ SetVertexShaderConstant%, GetVertexShaderConstant%, GetVertexShaderDeclaration%, \
\ GetVertexShaderFunction%, SetStreamSource%, GetStreamSource%, SetIndices%, \
\ GetIndices%, CreatePixelShader%, SetPixelShader%, GetPixelShader%, \
\ DeletePixelShader%, SetPixelShaderConstant%, GetPixelShaderConstant%, \
\ GetPixelShaderFunction%, DrawRectPatch%, DrawTriPatch%, DeletePatch%}
pDevice%=FN_initd3d(@hwnd%, 1, 1)
IF pDevice%=0 ERROR 100, "Couldn't create Direct3D8 device"
!(^D3Ddevice8{}+4) = !pDevice%
SYS `D3DXCreateSphere`, pDevice%, FN_f4(1), 50, 50, ^meshSphere%, 0
IF meshSphere% = 0 ERROR 100, "D3DXCreateSphere failed"
!(^D3Dbasemesh8{}+4) = !meshSphere%
REM. Point-source light:
D3Dlight8.Type%=1 : REM. point source
D3Dlight8.Diffuse.r% = FN_f4(1)
D3Dlight8.Diffuse.g% = FN_f4(1)
D3Dlight8.Diffuse.b% = FN_f4(1)
D3Dlight8.Specular.r% = FN_f4(1)
D3Dlight8.Specular.g% = FN_f4(1)
D3Dlight8.Specular.b% = FN_f4(1)
D3Dlight8.Position.x% = FN_f4(2)
D3Dlight8.Position.y% = FN_f4(1)
D3Dlight8.Position.z% = FN_f4(4)
D3Dlight8.Range% = FN_f4(10)
D3Dlight8.Attenuation0% = FN_f4(1)
REM. Material:
D3Dmaterial8.Diffuse.r% = FN_f4(0.2)
D3Dmaterial8.Diffuse.g% = FN_f4(0.6)
D3Dmaterial8.Diffuse.b% = FN_f4(1.0)
D3Dmaterial8.Specular.r% = FN_f4(0.4)
D3Dmaterial8.Specular.g% = FN_f4(0.4)
D3Dmaterial8.Specular.b% = FN_f4(0.4)
D3Dmaterial8.Power% = FN_f4(100)
fovy = RAD(30)
aspect = 5/4
znear = 1
zfar = 1000
bkgnd% = &7F7F7F
eyepos%() = 0, 0, FN_f4(6)
lookat%() = 0, 0, 0
up%() = 0, FN_f4(1), 0
SYS D3Ddevice8.Clear%, pDevice%, 0, 0, 3, bkgnd%, FN_f4(1), 0
SYS D3Ddevice8.BeginScene%, pDevice%
SYS D3Ddevice8.SetLight%, pDevice%, 0, D3Dlight8{}
SYS D3Ddevice8.LightEnable%, pDevice%, 0, 1
SYS D3Ddevice8.SetMaterial%, pDevice%, D3Dmaterial8{}
SYS D3Ddevice8.SetRenderState%, pDevice%, D3DRS_SPECULARENABLE, 1
SYS `D3DXMatrixLookAtLH`, ^mat%(0,0), ^eyepos%(0), ^lookat%(0), ^up%(0)
SYS D3Ddevice8.SetTransform%, pDevice%, D3DTS_VIEW, ^mat%(0,0)
SYS `D3DXMatrixPerspectiveFovLH`, ^mat%(0,0), FN_f4(fovy), \
\ FN_f4(aspect), FN_f4(znear), FN_f4(zfar)
SYS D3Ddevice8.SetTransform%, pDevice%, D3DTS_PROJECTION, ^mat%(0,0)
SYS D3Dbasemesh8.DrawSubset%, meshSphere%, 0
SYS D3Ddevice8.EndScene%, pDevice%
SYS D3Ddevice8.Present%, pDevice%, 0, 0, 0, 0
SYS D3Ddevice8.Release%, pDevice%
SYS D3Dbasemesh8.Release%, meshSphere%
SYS "FreeLibrary", d3dx%
END
- Output:
DarkBASIC
Some simple 3D objects are built into DarkBASIC. Creating a sphere only takes 1 line:
MAKE OBJECT SPHERE 1,1FreeBASIC
' "\" = a integer division (CPU)
' "/" = a floating point division (FPU)
' the compiler takes care of the conversion between floating point and integer
' compile with: FBC -s console "filename.bas" or FBC -s GUI "filename.bas"
' filename is whatever name you give it, .bas is mandatory
' Sphere using XPL0 code from rosetacode sphere page
' Altered freebasic version to compile in default mode
' version 17-06-2015
' compile with: fbc -s console or fbc -s gui
#Define W 640
#Define H 480
ScreenRes W, H, 32 ' set 640x480x32 graphics mode, 32 bits color mode
WindowTitle "32 bpp Cyan Sphere FreeBASIC"
' wait until keypress
' Color(RGB(255,255,255),RGB(0,0,0)) ' default white foreground, black background
Locate 50,2
Print "Enter any key to start"
Sleep
Dim As UInteger R = 100, R2 = R * R ' radius, in pixels; radius squared
Dim As UInteger X0 = W \ 2, Y0 = H \ 2 ' coordinates of center of screen
Dim As Integer X, Y, C, D2 ' coords, color, distance from center squared
For Y = -R To R ' for all the coordinates near the circle
For X = -R To R ' which is under the sphere
D2 = X * X + Y * Y
If D2 <= R2 Then ' coordinate is inside circle under sphere
' height of point on surface of sphere above X,Y
C = Sqr(R2 - D2) - ( X + Y) / 2 + 130 ' color is proportional; offset X and Y, and
Color C Shl 8 + C ' = color RGB(0, C, C)
' green + blue = cyan
PSet(X + X0, Y + Y0)
End If
Next
Next
' wait until keypress
Locate 50,2
Color(RGB(255,255,255),RGB(0,0,0)) ' foreground color is changed
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
needs #Lang "fblite", #Lang "qb" or #Lang "deprecated" to compile.
'Sphere for FreeBASIC May 2015
'spherefb4.bas
'Sphere using XPL0 code from rosetacode sphere page
'
screenres 640,480,32 '\set 640x480x32 graphics mode
windowtitle "32 bpp Blue Sphere FreeBASIC"
'
' wait until keypress
locate 50,2
color(rgb(255,255,255),rgb(0,0,0))
Print "Enter any key to start"
sleep
R=100 : R2=R*R '\radius, in pixels; radius squared
X0=640/2 : Y0=480/2 '\coordinates of center of screen
dim as integer X, Y, Z, C, D2 '\coords, color, distance from center squared
'
for Y= -R to +R '\for all the coordinates near the circle
for X = -R to +R '\ which is under the sphere
D2 = X*X + Y*Y '
C = 0 '\default color is black
if D2 <= R2 then '\coordinate is inside circle under sphere
Z = sqr(R2-D2) '\height of point on surface of sphere above X,Y
C = Z-(X+Y)/2+130 ' \color is proportional; offset X and Y, and
endif
color c ' \ shift color to upper limit of its range
'\green + blue = cyan orginal line don't understand
Pset(X+X0, Y+Y0)
next x
next y
'
' wait until keypress
locate 50,2
color(rgb(255,255,255),rgb(0,0,0))
Print "Enter any key to exit "
sleep
END
Liberty BASIC
WindowWidth =420
WindowHeight =460
nomainwin
open "Sphere" for graphics_nsb_nf as #w
#w "down ; fill lightgray"
xS =200
yS =200
for radius =150 to 0 step -1
level$ =str$( int( 256 -256 *radius /150))
c$ =level$ +" " +level$ +" " +level$
#w "color "; c$
#w "backcolor "; c$
#w "place "; xS; " "; yS
xS =xS -0.5
yS =yS -0.2
#w "circlefilled "; radius
next radius
#w "flush"
wait
close #w
endLocomotive Basic
Translated from ERRE version, this will print a 39x20 text sphere onscreen. The variables in line 80 can be used to adjust size (r), spotlight (k), reflective light (ambient).
10 MODE 2:s$=".:!*oe&#%@"
20 DIM v(2),vec(2)
30 v(0)=30:v(1)=30:v(2)=-50
40 lung=SQR(v(0)*v(0)+v(1)*v(1)+v(2)*v(2))
50 v(0)=v(0)/lung
60 v(1)=v(1)/lung
70 v(2)=v(2)/lung
80 r=10:k=2:ambient=0.4
90 FOR i=INT(-r) TO INT(r)
100 x=i+0.5
110 FOR j=INT(-2*r) TO INT(2*r)
120 y=j/2+0.5
130 IF (x*x+y*y<=r*r) THEN GOSUB 1000 ELSE PRINT" ";
140 NEXT j
150 PRINT
160 NEXT i
170 END
1000 vec(0)=x
1010 vec(1)=y
1020 vec(2)=SQR(r*r-x*x-y*y)
1030 GOSUB 2000
1040 GOSUB 3000
1050 b=d^k+ambient
1060 intensity%=(1-b)*(LEN(s$)-1)
1070 IF (intensity%<0) THEN intensity%=0
1080 IF (intensity%>LEN(s$)-1) THEN intensity%=LEN(s$)-2
1090 PRINT MID$(s$,intensity%+1,1);
1100 RETURN
2000 lung=SQR(vec(0)*vec(0)+vec(1)*vec(1)+vec(2)*vec(2))
2010 vec(0)=vec(0)/lung
2020 vec(1)=vec(1)/lung
2030 vec(2)=vec(2)/lung
2040 RETURN
3000 d=v(0)*vec(0)+v(1)*vec(1)+v(2)*vec(2)
3010 IF d<0 THEN d=-d ELSE d=0
3020 RETURN
The program above can also be adapted to produce graphical output in MODE 2 instead:
10 MODE 2:ORIGIN 320,200:INK 0,0:INK 1,26
20 DIM v(2),vec(2)
30 v(0)=30:v(1)=30:v(2)=-50
40 lung=SQR(v(0)*v(0)+v(1)*v(1)+v(2)*v(2))
50 v(0)=v(0)/lung
60 v(1)=v(1)/lung
70 v(2)=v(2)/lung
80 r=180:k=1.5:ambient=0.03
90 FOR i=INT(-r) TO INT(r)
100 x=i
110 FOR j=INT(-2*r) TO INT(2*r)
120 y=j/2
130 IF (x*x+y*y<=r*r) THEN GOSUB 1000
140 NEXT j
160 NEXT i
170 END
1000 vec(0)=x
1010 vec(1)=y
1020 vec(2)=SQR(r*r-x*x-y*y)
1030 GOSUB 2000
1040 GOSUB 3000
1050 b=(d^k+ambient)/(1+ambient)
1060 IF b>rnd THEN PLOT x,-y
1100 RETURN
2000 lung=SQR(vec(0)*vec(0)+vec(1)*vec(1)+vec(2)*vec(2))
2010 vec(0)=vec(0)/lung
2020 vec(1)=vec(1)/lung
2030 vec(2)=vec(2)/lung
2040 RETURN
3000 d=v(0)*vec(0)+v(1)*vec(1)+v(2)*vec(2)
3010 IF d<0 THEN d=-d ELSE d=0
3020 RETURN
PureBasic
3D Sphere animation.
; Original by Comtois @ 28/03/06
;
; Updated/Formated by Fluid Byte @ March.24,2009
;
; http://www.purebasic.fr/english/viewtopic.php?p=281258#p281258
Declare CreateSphere(M,P)
Declare UpdateMesh()
#_SIZEVERT = 36
#_SIZETRIS = 6
#FULLSCREEN = 0
Structure VECTOR
X.f
Y.f
Z.f
EndStructure
Structure VERTEX
X.f
Y.f
Z.f
NX.f
NY.f
NZ.f
Color.l
U.f
V.f
EndStructure
Structure TRIANGLE
V1.w
V2.w
V3.w
EndStructure
Macro CALC_NORMALS
*PtrV\NX = *PtrV\X
*PtrV\NY = *PtrV\Y
*PtrV\NZ = *PtrV\Z
EndMacro
Global *VBuffer, *IBuffer
Global Meridian = 50, Parallele = 50, PasLength = 4, Length
Define EventID, i, NbSommet, CameraMode, Angle.f, Pas.f = 0.5
InitEngine3D() : InitSprite() : InitKeyboard()
Add3DArchive(GetTemporaryDirectory(),#PB_3DArchive_FileSystem)
Add3DArchive(#PB_Compiler_Home + "Examples\Sources\Data\",#PB_3DArchive_FileSystem)
If #FULLSCREEN
OpenScreen(800,600,32,"Sphere 3D")
Else
OpenWindow(0,0,0,800,600,"Sphere 3D",#PB_Window_SystemMenu | 1)
OpenWindowedScreen(WindowID(0),0,0,800,600,0,0,0)
EndIf
;-Texture
CreateImage(0,128,128)
StartDrawing(ImageOutput(0))
For i = 0 To 127 Step 4
Box(0,i,ImageWidth(0),2,RGB(255,255,255))
Box(0,i + 2,ImageWidth(0),2,RGB(0,0,155))
Next i
StopDrawing()
SaveImage(0,GetTemporaryDirectory() + "temp.bmp") : FreeImage(0)
;-Material
CreateMaterial(0,LoadTexture(0,"temp.bmp"))
RotateMaterial(0,0.1,#PB_Material_Animated)
;-Mesh
CreateSphere(Meridian,Parallele)
;-Entity
CreateEntity(0,MeshID(0),MaterialID(0))
ScaleEntity(0,60,60,60)
;-Camera
CreateCamera(0,0,0,100,100)
MoveCamera(0,0,0,-200)
CameraLookAt(0,EntityX(0),EntityY(0),EntityZ(0))
;-Light
AmbientColor(RGB(105, 105, 105))
CreateLight(0, RGB(255, 255, 55), EntityX(0) + 150, EntityY(0) , EntityZ(0))
CreateLight(1, RGB( 55, 255, 255), EntityX(0) - 150, EntityY(0) , EntityZ(0))
CreateLight(2, RGB( 55, 55, 255), EntityX(0) , EntityY(0) + 150, EntityZ(0))
CreateLight(3, RGB(255, 55, 255), EntityX(0) , EntityY(0) - 150, EntityZ(0))
; ----------------------------------------------------------------------------------------------------
; MAINLOOP
; ----------------------------------------------------------------------------------------------------
Repeat
If #FULLSCREEN = 0
Repeat
EventID = WindowEvent()
Select EventID
Case #PB_Event_CloseWindow : End
EndSelect
Until EventID = 0
EndIf
Angle + Pas
RotateEntity(0, Angle, Angle,Angle)
If PasLength > 0 : UpdateMesh() : EndIf
If ExamineKeyboard()
If KeyboardReleased(#PB_Key_F1)
CameraMode = 1 - CameraMode
CameraRenderMode(0, CameraMode)
EndIf
EndIf
RenderWorld()
FlipBuffers()
Until KeyboardPushed(#PB_Key_Escape)
; ----------------------------------------------------------------------------------------------------
; FUNCTIONS
; ----------------------------------------------------------------------------------------------------
Procedure CreateSphere(M,P)
; M = Meridian
; P = Parallele
; The radius is 1. Front to remove it later, it's just for the demo.
If M < 3 Or P < 2 : ProcedureReturn 0 : EndIf
Protected Normale.VECTOR, NbSommet, i, j, Theta.f, cTheta.f, sTheta.f
Protected Alpha.f, cAlpha.f, sAlpha.f, *PtrV.VERTEX, *PtrF.TRIANGLE, NbTriangle
NbSommet = 2 + ((M + 1) * P)
*VBuffer = AllocateMemory(#_SIZEVERT * Nbsommet)
For i = 0 To M
Theta = i * #PI * 2.0 / M
cTheta = Cos(theta)
sTheta = Sin(theta)
For j = 1 To P
Alpha = j * #PI / (P + 1)
cAlpha = Cos(Alpha)
sAlpha = Sin(Alpha)
*PtrV = *VBuffer + #_SIZEVERT * ((i * P) + (j - 1))
*PtrV\X = sAlpha * cTheta
*PtrV\Y = sAlpha * sTheta
*PtrV\Z = cAlpha
*PtrV\U = Theta / (2.0 * #PI)
*PtrV\V = Alpha / #PI
CALC_NORMALS
Next j
Next i
; Southpole
*PtrV = *VBuffer + #_SIZEVERT * ((M + 1) * P)
*PtrV\X = 0
*PtrV\Y = 0
*PtrV\Z = -1
*PtrV\U = 0
*PtrV\V = 0
CALC_NORMALS
; Northpole
*PtrV + #_SIZEVERT
*PtrV\X = 0
*PtrV\Y = 0
*PtrV\Z = 1
*PtrV\U = 0
*PtrV\V = 0
CALC_NORMALS
; Les facettes
NbTriangle = 4 * M * P
*IBuffer = AllocateMemory(#_SIZETRIS * NbTriangle)
*PtrF = *IBuffer
For i = 0 To M - 1
For j = 1 To P - 1
*PtrF\V1 = ((i + 1) * P) + j
*PtrF\V2 = ((i + 1) * P) + (j - 1)
*PtrF\V3 = (i * P) + (j - 1)
*PtrF + #_SIZETRIS
*PtrF\V3 = ((i + 1) * P) + j ;Recto
*PtrF\V2 = ((i + 1) * P) + (j - 1) ;Recto
*PtrF\V1 = (i * P) + (j - 1) ;Recto
*PtrF + #_SIZETRIS
*PtrF\V1 = i * P + j
*PtrF\V2 = ((i + 1) * P) + j
*PtrF\V3 = (i * P) + (j - 1)
*PtrF + #_SIZETRIS
*PtrF\V3 = i * P + j ;Recto
*PtrF\V2 = ((i + 1) * P) + j ;Recto
*PtrF\V1 = (i * P) + (j - 1) ;Recto
*PtrF + #_SIZETRIS
Next j
Next i
; The Poles
For i = 0 To M - 1
*PtrF\V3 = (M + 1) * P + 1
*PtrF\V2 = (i + 1) * P
*PtrF\V1 = i * P
*PtrF + #_SIZETRIS
*PtrF\V1 = (M + 1) * P + 1 ;Recto
*PtrF\V2 = (i + 1) * P ;Recto
*PtrF\V3 = i * P ;Recto
*PtrF + #_SIZETRIS
Next i
For i = 0 To M - 1
*PtrF\V3 = (M + 1) * P
*PtrF\V2 = i * P + (P - 1)
*PtrF\V1 = (i + 1) * P + (P - 1)
*PtrF + #_SIZETRIS
*PtrF\V1 = (M + 1) * P ;Recto
*PtrF\V2 = i * P + (P - 1) ;Recto
*PtrF\V3 = (i + 1) * P + (P - 1) ;Recto
*PtrF + #_SIZETRIS
Next i
If CreateMesh(0,100)
Protected Flag = #PB_Mesh_Vertex | #PB_Mesh_Normal | #PB_Mesh_UVCoordinate | #PB_Mesh_Color
SetMeshData(0,Flag,*VBuffer,NbSommet)
SetMeshData(0,#PB_Mesh_Face,*IBuffer,NbTriangle)
ProcedureReturn 1
EndIf
ProcedureReturn 0
EndProcedure
; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Procedure UpdateMesh()
Protected NbTriangle = 4 * Meridian * Parallele
Length + PasLength
If Length >= NbTriangle
PasLength = 0
Length = Nbtriangle
EndIf
SetMeshData(0,#PB_Mesh_Face,*IBuffer,Length)
EndProcedure
QBasic
SCREEN 13 ' enter high-color graphic mode
' sets palette colors B/N
FOR i = 0 TO 255
PALETTE 255 - i, INT(i / 4) + INT(i / 4) * 256 + INT(i / 4) * 65536
NEXT i
PALETTE 0, 0
' draw the sphere
FOR i = 255 TO 0 STEP -1
x = 50 + i / 3
y = 99
CIRCLE (x, y), i / 3, i
PAINT (x, y), i
NEXT i
' wait until keypress
DO: LOOP WHILE INKEY$ = ""
END
Run BASIC
'Run BASIC White Sphere, Black background
'runbasic.com
graphic #win, 300, 300
#win size(1)
R=100
R2=R*R
X0=300/2
Y0=300/2
for Y = -150 to 150
for X = -150 to 150
D2 = X*X + Y*Y
C = 0
if D2 <= R2 then Z = sqr(R2-D2) : C = int(Z-(X+Y)/2+130)
#win color(C,C,C)
#win set(X+X0, Y+Y0)
next X
next Y
render #win'This is a simple Circle
graphic #g, 300, 300 'create a graphic object
#g place(100,100) 'place the drawing pen at 100,100
#g circle(75) 'make a circle with radius 75
render #g 'show itSinclair ZX81 BASIC
Works with 1k of RAM. A screenshot of the output is here.
10 LET I=21
20 LET J=2
30 FOR K=-PI TO PI STEP 0.07
40 PLOT 21+I*SIN K,22+21*COS K
50 PLOT 21+21*SIN K,22+(I-1)*COS K
60 NEXT K
70 LET I=I-J
80 LET J=J+1
90 IF I>0 THEN GOTO 30
Batch File
Since Batch Files do not support floating point, the input parameters for drawing the sphere are limited to integers only. The k parameter has been hardcoded to 2. The ambient variable for this code is scaled up 10 times of its value in C implementation. For example, ambient = 0.1 in C code corresponds to ambient = 1 here.
Lastly, the variables used in calculations are scaled up 100 times of the actual values in C implementation, and then scaled down 100 times back for determination of shades.
:: Draw a Sphere Task from Rosetta Code
:: Batch File Implementation
@echo off
rem -------------- define arithmetic "functions"
rem more info: https://www.dostips.com/forum/viewtopic.php?f=3&t=6744
rem integer sqrt arithmetic function by Aacini, penpen and einstein1969
rem source: https://www.dostips.com/forum/viewtopic.php?f=3&t=5819&start=30#p44016
set "sqrt(N)=( M=(N),j=M/(11*1024)+40, j=(M/j+j)>>1, j=(M/j+j)>>1, j=(M/j+j)>>1, j=(M/j+j)>>1, j=(M/j+j)>>1, j+=(M-j*j)>>31 )"
rem -------------- define batch file macros with parameters appended
rem more info: https://www.dostips.com/forum/viewtopic.php?f=3&t=2518
setlocal disabledelayedexpansion % == required for macro ==%
(set \n=^^^
%== this creates escaped line feed for macro ==%
)
rem normalize macro
rem argument: v
set normalize=for %%# in (1 2) do if %%#==2 ( %\n%
for /f "tokens=1" %%a in ("!args!") do set "v=%%a" %\n%
set /a "length_sqrd=!v![0]*!v![0]+!v![1]*!v![1]+!v![2]*!v![2]" %\n%
set /a "length=%sqrt(N):N=!length_sqrd!%" %== sqrt(N) applied ==% %\n%
set /a "!v![0]*=100", "!v![1]*=100", "!v![2]*=100" %== normalized elements mult. by 100 ==% %\n%
set /a "!v![0]/=length", "!v![1]/=length", "!v![2]/=length" %\n%
) else set args=
rem dot macro
rem arguments: s t outputvar
set dot=for %%# in (1 2) do if %%#==2 ( %\n%
for /f "tokens=1,2,3" %%a in ("!args!") do ( %\n%
set "s=%%a" %\n%
set "t=%%b" %\n%
set "outputvar=%%c" %\n%
) %\n%
set /a "d=!s![0]*!t![0]+!s![1]*!t![1]+!s![2]*!t![2]" %\n%
if !d! lss 0 (set /a "!outputvar!=-d") else (set "!outputvar!=0") %\n%
) else set args=
rem -------------- define pseudo-arrays
set "shades[0]=."
set "shades[1]=:"
set "shades[2]=!"
set "shades[3]=*"
set "shades[4]=o"
set "shades[5]=e"
set "shades[6]=&"
set "shades[7]=#"
set "shades[8]=%%"
set "shades[9]=@"
set "num_shades=9" %== start at 0 ==%
set "light[0]=30" & set "light[1]=30" & set "light[2]=-50"
rem -------------- main thing: execute drawSphere
setlocal enabledelayedexpansion
%normalize% light %== normalize macro applied ==%
call :drawSphere 20 1
exit /b 0
rem -------------- the function to draw the sphere
rem arguments: R ambient
:drawSphere
rem initialize variables from arguments
set /a "R=%1", "negR=-R", "twiceR=R*2", "twiceNegR=negR*2"
set /a "sqrdR=R*R*100*100" %== R*R is mult. by 100*100 ==%
set "k=2" %== k is hardcoded to 2 ==%
set "ambient=%2"
rem start draw line-by-line
for /l %%i in (%negR%, 1, %R%) do (
set /a "x=100*%%i+(100/2)" %== x is mult. by 100 ==%
set "line="
for /l %%j in (%twiceNegR%, 1, %twiceR%) do (
set /a "y=(100/2)*%%j+(100/2)" %== y is mult. by 100 ==%
set /a "pythag = x*x + y*y"
if !pythag! lss !sqrdR! (
set /a "vec[0]=x"
set /a "vec[1]=y"
set /a "vec[2]=sqrdR-pythag"
set /a "vec[2]=%sqrt(N):N=!vec[2]!%" %== sqrt(N) applied ==%
%normalize% vec %== normalize macro applied ==%
%dot% light vec dot_out %== dot macro applied ==%
rem since both light and vec are normalized to 100,
rem then dot_out is scaled up by 100*100 now.
set /a "dot_out/=100" %== scale-down to 100*[actual] to prevent overflow before exponentiation ==%
set "scaleup=1" %== after exponentiation, b would be scaleup*[actual] ==%
set "b=1"
for /l %%? in (1,1,%k%) do set /a "b*=dot_out","scaleup*=100" %== exponentiation ==%
set /a "b+=ambient*scaleup/10" %== add ambient/10 to b ==%
set /a "b/=scaleup/100" %== scale-down to 100*[actual] ==%
set /a "intensity=(100-b)*num_shades"
set /a "intensity/=100" %== final scale-down ==%
if !intensity! lss 0 set "intensity=0"
if !intensity! gtr %num_shades% set "intensity=%num_shades%"
for %%c in (!intensity!) do set "line=!line!!shades[%%c]!"
) else (
set "line=!line! "
)
)
echo(!line!
)
goto :EOF
- Output:
eeeeeeeeee&&&&&##
eoooo*****ooooooooeeeee&&&&###%
oo******!!!!!********oooooeeee&&&&###%%
o**!!!!!!!!!!!!!!!!!!*****oooooeeee&&&&###%%%
o**!!!!:::::::::::!!!!!!!!!****oooooeee&&&&&###%%%%
o*!!!:::::::::::::::::::!!!!!!*****ooooeeee&&&&####%%%%
o*!!!:::::........:::::::::!!!!!!*****oooeeee&&&&&####%%%%@
o*!!!::::.............::::::::!!!!!!****ooooeeee&&&&####%%%%%@@
**!!::::.................::::::!!!!!!*****ooooeeee&&&&####%%%%%%@
e*!!!::::..................:::::::!!!!!!****ooooeeee&&&&#####%%%%%@@@
o*!!!:::....................::::::!!!!!!!****ooooeeee&&&&&####%%%%%%@@@
e**!!::::....................::::::!!!!!!*****ooooeeee&&&&#####%%%%%%@@@@
e**!!!::::..................::::::::!!!!!!****ooooeeeee&&&&#####%%%%%%%@@@@
o**!!:::::..................:::::::!!!!!!*****ooooeeeee&&&&#####%%%%%%%@@@@
eo*!!!::::::...............::::::::!!!!!!*****ooooeeeee&&&&&#####%%%%%%%@@@@@
o**!!!!:::::::.........::::::::::!!!!!!!*****oooooeeee&&&&&&####%%%%%%%%@@@@@
eo**!!!!!:::::::::::::::::::::::!!!!!!!!*****oooooeeeee&&&&&#####%%%%%%%%@@@@@@
eoo**!!!!!::::::::::::::::::::!!!!!!!!******oooooeeeee&&&&&######%%%%%%%@@@@@@@
eoo***!!!!!:::::::::::::::::!!!!!!!!*******ooooeeeeee&&&&&######%%%%%%%%@@@@@@@
eoo****!!!!!!!!!!:::!:!!!!!!!!!!!!*******oooooeeeeee&&&&&######%%%%%%%%@@@@@@@@
eeoo****!!!!!!!!!!!!!!!!!!!!!!!!********oooooeeeeee&&&&&&#####%%%%%%%%%@@@@@@@@
&eeoo******!!!!!!!!!!!!!!!!!*********ooooooeeeeee&&&&&&######%%%%%%%%%@@@@@@@@@
&eeeooo********!*!!!!!************oooooooeeeeeee&&&&&&######%%%%%%%%%@@@@@@@@@@
#&eeeooooo********************ooooooooeeeeeeee&&&&&&#######%%%%%%%%%@@@@@@@@@@@
&&eeeeoooooooo*********oooooooooooeeeeeeee&&&&&&&&######%%%%%%%%%%@@@@@@@@@@@
#&&&eeeeeooooooooooooooooooooooeeeeeeeee&&&&&&&&#######%%%%%%%%%%@@@@@@@@@@@@
#&&&&eeeeeeeeoooooooooeeeeeeeeeeeeee&&&&&&&&########%%%%%%%%%%@@@@@@@@@@@@@
%##&&&&&eeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&&########%%%%%%%%%%%@@@@@@@@@@@@@@
%###&&&&&&&&eeeeeeeeeeeee&&&&&&&&&&&&&########%%%%%%%%%%%%@@@@@@@@@@@@@@@
%%####&&&&&&&&&&&&&&&&&&&&&&&&&&###########%%%%%%%%%%%%%@@@@@@@@@@@@@@@
%%%#######&&&&&&&&&&&&&&&&#############%%%%%%%%%%%%%%@@@@@@@@@@@@@@@@
%%%##############################%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@@@
%%%%%%%####################%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@@@@@
@%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@@@@@@@
@@%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@%%%%%%%%%%%@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@
Befunge
While based on the C implementation, the algorithm has been considerably simplified to try and avoid floating point (which Befunge doesn't support) and minimise the need for sqrt calculations (which we approximate using the Babylonian method).
The first four values on the stack define the radius (45* = 20) and the light vector (65*65*"2" = 30;30;50). The k parameter has been hardcoded to 2, and the ambient light is approximated by adjusting the shade characters (defined on the last line).
Also note that the z-coordinate of the light vector is negated at runtime to more closely match the C defaults. This is preferable to making the initial constant negative since negative data values aren't supported across all Befunge implementations.
45*65*65*"2"30p20p10p::00p2*40p4*5vv<
>60p140g->:::*00g50g*60g40g-:*-\-v0>1
^_@#`\g0<|`\g04:+1, <*84$$_v#`\0:<>p^
>v>g2+:5^$>g:*++*/7g^>*:9$#<"~"/:"~"v
g:^06,+55<^03*<v09p07%"~"p09/"~"p08%<
^>#0 *#12#<0g:^>+::"~~"90g*80g+*70gv|
g-10g*+:9**00gv|!*`\2\`-20::/2-\/\+<>
%#&eo*!:..^g05<>$030g-*9/\20g*+60g40^
- Output:
eeeeeeeeeee&&&&&#
eooo********oooooooeeee&&&&###%
oo****!!!!!!!!********ooooeeeee&&&###%%
o**!!!!!!!!!!!!!!!!!!!*****oooooeeee&&&####%%
o*!!!!:::::::::::::::!!!!!!*****ooooeeee&&&&####%%%
**!!:::::::....::::::::::!!!!!!****ooooeeeee&&&####%%%%
**!!::::.............::::::::!!!!!****ooooeeee&&&&####%%%%%
o*!!::::.................::::::!!!!!!****ooooeeee&&&&####%%%%%%
*!!::::....................::::::!!!!!****ooooeeeee&&&&####%%%%%%
e*!!:::......................::::::!!!!!*****ooooeeee&&&&####%%%%%%%%
o*!!:::.......................::::::!!!!!*****ooooeeee&&&&#####%%%%%%%%
o*!!::::.......................::::::!!!!!****oooooeeee&&&&#####%%%%%%%%%
e**!!:::.......................::::::!!!!!*****ooooeeeee&&&&#####%%%%%%%%%%
o*!!!:::......................:::::::!!!!!*****ooooeeeee&&&&#####%%%%%%%%%%
o**!!!::::...................::::::::!!!!!*****oooooeeee&&&&&#####%%%%%%%%%%%
o**!!!:::::................::::::::!!!!!!*****oooooeeeee&&&&#####%%%%%%%%%%%%
eo**!!!:::::::............:::::::::!!!!!!*****oooooeeeee&&&&&#####%%%%%%%%%%%%%
eo***!!!:::::::::::::::::::::::::!!!!!!******oooooeeeee&&&&&#####%%%%%%%%%%%%%%
eoo**!!!!!::::::::::::::::::::!!!!!!!!******oooooeeeee&&&&&######%%%%%%%%%%%%%%
eoo***!!!!!!:::::::::::::::!!!!!!!!!******ooooooeeeee&&&&&######%%%%%%%%%%%%%%%
eeoo****!!!!!!!!!!!!!!!!!!!!!!!!!*******ooooooeeeeee&&&&&######%%%%%%%%%%%%%%%%
&eooo*****!!!!!!!!!!!!!!!!!!!!********ooooooeeeeee&&&&&&######%%%%%%%%%%%%%%%%%
&eeoooo*******!!!!!!!!!!***********oooooooeeeeeee&&&&&&######%%%%%%%%%%%%%%%%%#
&&eeeoooo***********************ooooooooeeeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%#
&&eeeooooooo**************ooooooooooeeeeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%#
#&&eeeeeoooooooooooooooooooooooooeeeeeeee&&&&&&&########%%%%%%%%%%%%%%%%%%%##
#&&&eeeeeeeooooooooooooooooeeeeeeeeee&&&&&&&&########%%%%%%%%%%%%%%%%%%%%##
%##&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&&########%%%%%%%%%%%%%%%%%%%%%##&
%###&&&&&&eeeeeeeeeeeeeeeeee&&&&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%##&
%####&&&&&&&&&&&&&&&&&&&&&&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%##&
%%######&&&&&&&&&&&&&&&&&&&&############%%%%%%%%%%%%%%%%%%%%%%%%%%##e
%%%################################%%%%%%%%%%%%%%%%%%%%%%%%%%%##&
%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###&
%%%%%%%%%###########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###&
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###&
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%##&&
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###&
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%####&
%%%%%%%%%%%%%%%%%%%%%%%%%%####&
%%%%%%%%%%%%#####
Brlcad
opendb balls.g y # Create a database to hold our shapes
units cm # Set the unit of measure
in ball.s sph 0 0 0 3 # Create a sphere of radius 3 cm named ball.s with its centre at 0,0,0C
The lighting calculation is somewhere between crude and bogus, but hey, I'm shading it with ASCII characters, don't expect too much.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include <math.h>
const char *shades = ".:!*oe&#%@";
double light[3] = { 30, 30, -50 };
void normalize(double * v)
{
double len = sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
v[0] /= len; v[1] /= len; v[2] /= len;
}
double dot(double *x, double *y)
{
double d = x[0]*y[0] + x[1]*y[1] + x[2]*y[2];
return d < 0 ? -d : 0;
}
void draw_sphere(double R, double k, double ambient)
{
int i, j, intensity;
double b;
double vec[3], x, y;
for (i = floor(-R); i <= ceil(R); i++) {
x = i + .5;
for (j = floor(-2 * R); j <= ceil(2 * R); j++) {
y = j / 2. + .5;
if (x * x + y * y <= R * R) {
vec[0] = x;
vec[1] = y;
vec[2] = sqrt(R * R - x * x - y * y);
normalize(vec);
b = pow(dot(light, vec), k) + ambient;
intensity = (1 - b) * (sizeof(shades) - 1);
if (intensity < 0) intensity = 0;
if (intensity >= sizeof(shades) - 1)
intensity = sizeof(shades) - 2;
putchar(shades[intensity]);
} else
putchar(' ');
}
putchar('\n');
}
}
int main()
{
normalize(light);
draw_sphere(20, 4, .1);
draw_sphere(10, 2, .4);
return 0;
}
- Output:
#############%%%%
##&&eeeeeeeeee&&&&&&&####%%%%%%%%
&&eeooooooooooooooeeeee&&&&######%%%%%%%%
eeoo**************oooooooeeee&&&&####%%%%%%%%
&&oo**!!!!!!::!!!!!!!!****oooooee&&&&######%%%%%%%%%%
eeoo!!!!::::::::::::::!!!!*****ooeeee&&&&####%%%%%%%%%%%%
ee**!!::::............::::!!!!***ooooeeee&&######%%%%%%%%%%%%
&&oo!!::..................::!!!!*****ooeeee&&&&####%%%%%%%%%%%%%%
oo!!::....................::::!!*****ooeeee&&&&####%%%%%%%%%%%%%%
ee**!!::....................::::!!*****ooeeee&&&&####%%%%%%%%%%%%%%%%
&&oo!!::......................::::!!*****ooeeee&&&&######%%%%%%%%%%%%%%%%
ee**!!::......................::::!!*****ooeeee&&&&######%%%%%%%%%%%%%%%%
##oo**!!::......................::!!!!*****ooeeee&&&&####%%%%%%%%%%%%%%%%%%%%
&&oo**::::....................::::!!!!***ooooeeee&&&&####%%%%%%%%%%%%%%%%%%%%
eeoo**!!::..................::::!!!!*****ooooee&&&&######%%%%%%%%%%%%%%%%%%%%
eeoo**!!::................::::!!!!****oooooeeee&&&&######%%%%%%%%%%%%%%%%%%%%
#eeoo**!!::::............::::!!!!!!****oooeeee&&&&&&######%%%%%%%%%%%%%%%%%%%%%%
#eeoo**!!!!::::::::::::::::!!!!!!****oooooeeee&&&&######%%%%%%%%%%%%%%%%%%%%%%%%
#eeoooo**!!!!!!::::::::!!!!!!******ooooeeeee&&&&&&######%%%%%%%%%%%%%%%%%%%%%%%%
#&&eeoo****!!!!!!!!!!!!!!!!******ooooeeeee&&&&&&######%%%%%%%%%%%%%%%%%%%%%%%%%%
#&&eeoooo********************ooooooeeee&&&&&&&######%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#&&&&eeoooooo************ooooooeeeeee&&&&&&&########%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%##&&eeeeeeooooooooooooooooooeeeeee&&&&&&&########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%####&&&&eeeeeeeeeeeeeeeeeeeeee&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%##&&&&&&eeeeeeeeeeeeeeee&&&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%######&&&&&&&&&&&&&&&&&&&&&&&&###########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%########&&&&&&&&&&&&&&############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%##############################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%######################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%####%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::..:::::!!**
.............::!!**oo
...................::!!**ooee
.......................::!!ooeeee
.......................::!!**ooee
.........................::!!**ooeeee
.........................::!!**ooeeee
:.........................::!!**ooeeeeee
........................::!!**ooooeeeeee
:.......................::!!**ooeeeeeeee
:.....................::!!****ooeeeeeeee
!::................:::!!****ooeeeeeeeeee
*!!::..........::::!!!****ooooeeeeeeeeee
**!!::::::::::!!!!*****ooooeeeeeeeeee
oo**!!!!!!!!!!*******ooooeeeeeeeeeeee
oooo********oooooooeeeeeeeeeeeeee
eeeeooooooooooeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
Fun with 3D noise texture
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define MAXD 8
int g[] = { -1, 1, -1, 1 };
/* Perlin-like noise */
static inline void
hashed(int *data, int *out, int len) {
# define ror(a, d) ((a << (d)) | (a >> (32 - d)))
register unsigned int h = 0x12345678, tmp;
unsigned int *d = (void*)data;
int i = len;
while (i--) {
tmp = *d++;
h += ror(h, 15) ^ ror(tmp, 5);
}
h ^= ror(h, 7);
h += ror(h, 23);
h ^= ror(h, 19);
h += ror(h, 11);
h ^= ror(h, 13);
h += ror(h, 17);
# undef ror
for (i = len; i--; ) {
out[i] = g[h & 3];
h >>= 2;
}
}
double scale[MAXD], scale_u[MAXD];
void noise_init()
{
int i;
for (i = 1; i < MAXD; i++) {
scale[i] = 1 / (1 + sqrt(i + 1));
scale_u[i] = scale[i] / sqrt(i + 1);
}
}
double noise(double *x, int d)
{
# define sum(s, x) for (s = 0, j = 0; j < d; j++) s += x
register int i, j;
int n[MAXD], o[MAXD], g[MAXD], tmp;
double s, r, t, w, ret, u[MAXD];
sum(s, x[j]);
s *= scale[d];
for (i = 0; i < d; i++) {
o[i] = i;
t = x[i] + s;
u[i] = t - (n[i] = floor(t));
}
o[d] = 0;
for (i = 0; i < d - 1; i++)
for (j = i; j < d; j++)
if (u[o[i]] < u[o[j]])
tmp = o[i], o[i] = o[j], o[j] = tmp;
ret = w = 0, r = 1;
for (s = 0, j = 0; j < d; j++) s += n[j];
s *= scale_u[d];
for (i = 0; i <= d; i++) {
for (j = 0; j < d; j++)
u[j] = x[j] + s - n[j];
for (t = (d + 1.) / (2 * d), j = 0; j < d; j++) {
t -= u[j] * u[j];
if (t <= 0) break;
}
if (t >= 0) {
r = 0;
hashed(n, g, d);
for (j = 0; j < d; j++)
if (g[j]) r += (g[j] == 1 ? u[j] : -u[j]);
t *= t;
ret += r * t * t;
}
if (i < d) {
n[o[i]]++;
s += scale_u[d];
}
}
return ret * (d * d);
}
double get_noise2(double x, double y)
{
int i, ws;
double r = 0, v[2];
for (i = 1, ws = 0; i <= 128; i <<= 1) {
v[0] = x * i, v[1] = y * i;
r += noise(v, 2);
ws ++;
}
r /= ws;
return r;
}
double get_noise3(double x, double y, double z)
{
int i, ws;
double r = 0, v[3], w;
for (i = 1, ws = 0; i <= 32; i <<= 1) {
v[0] = x * i, v[1] = y * i, v[2] = z * i;
w = 1./sqrt(i);
r += noise(v, 3) * w;
ws += w;
}
return r / ws;
}
int main(int c, char** v)
{
unsigned char pix[256 * 256], *p;
int i, j;
double x, y, z, w;
FILE *fp;
noise_init();
for (p = pix, i = 0; i < 256 * 256; i++) *p++ = 0;
for (p = pix, i = 0; i < 256; i++) {
y = (i - 128) / 125.;
for (j = 0; j < 256; j++, p++) {
x = (j - 128) / 125.;
*p = (get_noise2(i/256., j/256.) + 1) / 6 * i;
z = 1- x*x - y*y;
if (z < 0) continue;
z = sqrt(z);
w = get_noise3(x, y, z);
w = (w + 1) / 2;
w *= (1 + x - y + z) / 3.5;
if (w < 0) w = 0;
*p = w * 255;
}
}
fp = fopen("out.pgm", "w+");
fprintf(fp, "P5\n256 256\n255\n");
fwrite(pix, 1, 256 * 256, fp);
fclose(fp);
return 0;
}
C#
using System;
namespace Sphere {
internal class Program {
private const string Shades = ".:!*oe%&#@";
private static readonly double[] Light = {30, 30, -50};
private static void Normalize(double[] v) {
double len = Math.Sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
v[0] /= len;
v[1] /= len;
v[2] /= len;
}
private static double Dot(double[] x, double[] y) {
double d = x[0]*y[0] + x[1]*y[1] + x[2]*y[2];
return d < 0 ? -d : 0;
}
public static void DrawSphere(double r, double k, double ambient) {
var vec = new double[3];
for(var i = (int)Math.Floor(-r); i <= (int)Math.Ceiling(r); i++) {
double x = i + .5;
for(var j = (int)Math.Floor(-2*r); j <= (int)Math.Ceiling(2*r); j++) {
double y = j/2.0 + .5;
if(x*x + y*y <= r*r) {
vec[0] = x;
vec[1] = y;
vec[2] = Math.Sqrt(r*r - x*x - y*y);
Normalize(vec);
double b = Math.Pow(Dot(Light, vec), k) + ambient;
int intensity = (b <= 0)
? Shades.Length - 2
: (int)Math.Max((1 - b)*(Shades.Length - 1), 0);
Console.Write(Shades[intensity]);
}
else
Console.Write(' ');
}
Console.WriteLine();
}
}
private static void Main() {
Normalize(Light);
DrawSphere(6, 4, .1);
DrawSphere(10, 2, .4);
Console.ReadKey();
}
}
}
C++
// Based on https://www.cairographics.org/samples/gradient/
#include <QImage>
#include <QPainter>
int main() {
const QColor black(0, 0, 0);
const QColor white(255, 255, 255);
const int size = 300;
const double diameter = 0.6 * size;
QImage image(size, size, QImage::Format_RGB32);
QPainter painter(&image);
painter.setRenderHint(QPainter::Antialiasing);
QLinearGradient linearGradient(0, 0, 0, size);
linearGradient.setColorAt(0, white);
linearGradient.setColorAt(1, black);
QBrush brush(linearGradient);
painter.fillRect(QRect(0, 0, size, size), brush);
QPointF point1(0.4 * size, 0.4 * size);
QPointF point2(0.45 * size, 0.4 * size);
QRadialGradient radialGradient(point1, size * 0.5, point2, size * 0.1);
radialGradient.setColorAt(0, white);
radialGradient.setColorAt(1, black);
QBrush brush2(radialGradient);
painter.setPen(Qt::NoPen);
painter.setBrush(brush2);
painter.drawEllipse(QRectF((size - diameter)/2, (size - diameter)/2, diameter, diameter));
image.save("sphere.png");
return 0;
}
- Output:
Clojure
(use 'quil.core)
(def w 500)
(def h 400)
(defn setup []
(background 0))
(defn draw []
(push-matrix)
(translate 250 200 0)
(sphere 100)
(pop-matrix))
(defsketch main
:title "sphere"
:setup setup
:size [w h]
:draw draw
:renderer :opengl)
- Output:
![[1]](http://i.imgur.com/fkzH5wM.png){kind=link}
Common Lisp
Saved as a png file and rendered in a X-Window. Unfortunately the file upload isn't working anymore for like four years so I cannot show my results directly.
;; * Loading the cairo bindings
(eval-when (:compile-toplevel :load-toplevel)
(ql:quickload '("cl-cairo2" "cl-cairo2-xlib")))
;; * The package definition
(defpackage :sphere
(:use :common-lisp :cl-cairo2))
(in-package :sphere)
(defparameter *context* nil)
(defparameter *size* 400)
(defparameter *middle* (/ *size* 2))
;; Opening a display and draw a sphere
(let ((width *size*)
(height *size*))
;; Draw to a X-Window
(setf *context*
(create-xlib-image-context width height :window-name "Sphere"))
;; Clear the whole canvas with gray
(rectangle 0 0 width height)
(set-source-rgb 127 127 127)
(fill-path)
;; Draw a the sphere as circa with a radial pattern
(with-patterns ((pat (create-radial-pattern (* 0.9 *middle*) (* 0.8 *middle*) (* 0.2 *middle*)
(* 0.8 *middle*) (* 0.8 *middle*) *middle*)))
(pattern-add-color-stop-rgba pat 0 1 1 1 1)
(pattern-add-color-stop-rgba pat 1 0 0 0 1)
(set-source pat)
(arc *middle* *middle* 180 0 (* 2 pi))
(fill-path))
;; Draw to a png file
(with-png-file ("sphere.png" :rgb24 width height)
;; Clear the whole canvas with gray
(rectangle 0 0 width height)
(set-source-rgb 127 127 127)
(fill-path)
;; Draw a the sphere as circa with a radial pattern
(with-patterns ((pat (create-radial-pattern (* 0.9 *middle*) (* 0.8 *middle*) (* 0.2 *middle*)
(* 0.8 *middle*) (* 0.8 *middle*) *middle*)))
(pattern-add-color-stop-rgba pat 0 1 1 1 1)
(pattern-add-color-stop-rgba pat 1 0 0 0 1)
(set-source pat)
(arc *middle* *middle* 180 0 (* 2 pi))
(fill-path))))
ContextFree
startshape SPHERE
shape SPHERE {
CIRCLE[]
SPHERE[x 0.1% y 0.1%s 0.99 0.99 b 0.05]
}Craft Basic
let j = 2
for i = 221 to 0 step j * -1
for k = -3.14 to 3.14 step .01
dot 221 + i * sin(k), 222 + 221 * cos(k)
dot 221 + 221 * sin(k), 222 + (i - 1) * cos(k)
wait
next k
let j = j + 1
next i
D
import std.stdio, std.math, std.algorithm, std.numeric;
alias V3 = double[3];
immutable light = normalize([30.0, 30.0, -50.0]);
V3 normalize(V3 v) pure @nogc {
v[] /= dotProduct(v, v) ^^ 0.5;
return v;
}
double dot(in ref V3 x, in ref V3 y) pure nothrow @nogc {
immutable double d = dotProduct(x, y);
return d < 0 ? -d : 0;
}
void drawSphere(in double R, in double k, in double ambient) @nogc {
enum shades = ".:!*oe&#%@";
foreach (immutable i; cast(int)floor(-R) .. cast(int)ceil(R) + 1) {
immutable double x = i + 0.5;
foreach (immutable j; cast(int)floor(-2 * R) ..
cast(int)ceil(2 * R) + 1) {
immutable double y = j / 2. + 0.5;
if (x ^^ 2 + y ^^ 2 <= R ^^ 2) {
immutable vec = [x, y, (R^^2 - x^^2 - y^^2) ^^ 0.5]
.normalize;
immutable double b = dot(light, vec) ^^ k + ambient;
int intensity = cast(int)((1 - b) * (shades.length-1));
intensity = min(shades.length - 1, max(intensity, 0));
shades[intensity].putchar;
} else
' '.putchar;
}
'\n'.putchar;
}
}
void main() {
drawSphere(20, 4, 0.1);
drawSphere(10, 2, 0.4);
}
Delphi
Under Microsoft Windows: If you notice the big sphere loses its roundness, then try increasing the width of the Windows console. By default it’s 80; so put it to something bigger, let’s say 90.
Steps: Run the CMD Windows shell. Then follow this path to setup the new width: Main Menu-> Properties -> Layout -> Window Size -> Width.
program DrawASphere;
{$APPTYPE CONSOLE}
uses
SysUtils,
Math;
type
TDouble3 = array[0..2] of Double;
TChar10 = array[0..9] of Char;
var
shades: TChar10 = ('.', ':', '!', '*', 'o', 'e', '&', '#', '%', '@');
light: TDouble3 = (30, 30, -50 );
procedure normalize(var v: TDouble3);
var
len: Double;
begin
len:= sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
v[0] := v[0] / len;
v[1] := v[1] / len;
v[2] := v[2] / len;
end;
function dot(x, y: TDouble3): Double;
begin
Result:= x[0]*y[0] + x[1]*y[1] + x[2]*y[2];
Result:= IfThen(Result < 0, -Result, 0 );
end;
procedure drawSphere(R, k, ambient: Double);
var
vec: TDouble3;
x, y, b: Double;
i, j,
intensity: Integer;
begin
for i:= Floor(-R) to Ceil(R) do
begin
x := i + 0.5;
for j:= Floor(-2*R) to Ceil(2 * R) do
begin
y:= j / 2 + 0.5;
if(x * x + y * y <= R * R) then
begin
vec[0]:= x;
vec[1]:= y;
vec[2]:= sqrt(R * R - x * x - y * y);
normalize(vec);
b:= Power(dot(light, vec), k) + ambient;
intensity:= IfThen(b <= 0,
Length(shades) - 2,
Trunc(max( (1 - b) * (Length(shades) - 1), 0 )));
Write(shades[intensity]);
end
else
Write(' ');
end;
Writeln;
end;
end;
begin
normalize(light);
drawSphere(19, 4, 0.1);
drawSphere(10, 2, 0.4);
Readln;
end.
- Output:
&&&&&&&&&&#######
&eeeeeooeeeeeeee&&&&&&#######
eeooo*********oooooeeeee&&&&&#######%
eo***!!!!!!!!!!!*****ooooeeee&&&&&#######%%
eo**!!!::::::::::!!!!!****ooooeeee&&&&########%%%
eo*!!::::........:::::!!!!****oooeeee&&&&########%%%%
eo*!!::..............:::::!!!***ooooeeee&&&&#########%%%%
eo*!!::..................:::!!!!***oooeeee&&&&&########%%%%%%
eo*!::....................::::!!!***ooooeeee&&&&#########%%%%%%
o**!::.....................::::!!!***ooooeeee&&&&#########%%%%%%%
eo*!::......................::::!!!***ooooeeee&&&&##########%%%%%%%
eo*!!::......................:::!!!!***ooooeee&&&&&##########%%%%%%%%
eo**!!::.....................:::!!!!***ooooeeee&&&&&##########%%%%%%%%%
&eo**!!::...................::::!!!!****oooeeeee&&&&&##########%%%%%%%%%%
eeo**!!:::................:::::!!!!****ooooeeee&&&&&##########%%%%%%%%%%%
&eoo**!!!::::............:::::!!!!****oooooeeee&&&&&###########%%%%%%%%%%%%
&eeo***!!!::::::::::::::::::!!!!!****ooooeeeee&&&&&&##########%%%%%%%%%%%%%
&eeoo***!!!!::::::::::::!!!!!!*****oooooeeeee&&&&&&###########%%%%%%%%%%%%%
&&eeoo****!!!!!!!!!!!!!!!!!!*****oooooeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeeooo*****!!!!!!!!!!*******ooooooeeeeee&&&&&&############%%%%%%%%%%%%%%%
#&&eeeoooo*****************oooooooeeeeee&&&&&&&############%%%%%%%%%%%%%%%%
#&&&eeeeoooooooooooooooooooooooeeeeeee&&&&&&&#############%%%%%%%%%%%%%%%%%
##&&&&eeeeeoooooooooooooooeeeeeeeee&&&&&&&&##############%%%%%%%%%%%%%%%%%%
###&&&&eeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%
####&&&&&&&eeeeeeeeeeeeeee&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%
#####&&&&&&&&&&&&&&&&&&&&&&&&&&&&#################%%%%%%%%%%%%%%%%%%%%%
########&&&&&&&&&&&&&&&&&&&####################%%%%%%%%%%%%%%%%%%%%%%
############################################%%%%%%%%%%%%%%%%%%%%%%%
%#######################################%%%%%%%%%%%%%%%%%%%%%%%%%
%%##################################%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%###########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%#################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::...:::!!!*o
..............::!!*oo
..................::!!**ooe
.....................::!!**ooee
.......................::!!**ooee
........................::!!**oooee
.........................::!!**oooeee
:........................::!!!**oooeeee
........................::!!!**ooooeeee
:......................::!!!***oooeeeee
:....................:::!!!***oooeeeeee
!:.................:::!!!****oooeeeeeee
*!:::...........::::!!!!***ooooeeeeeeee
*!!!:::::::::::!!!!!****oooooeeeeeeee
o**!!!!!!!!!!!!!*****oooooeeeeeeeee
oo**************ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
DWScript
but adapted to spit out a PGM image
type
TFloat3 = array[0..2] of Float;
var
light : TFloat3 = [ 30, 30, -50 ];
procedure normalize(var v : TFloat3);
var
len: Float;
begin
len := sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
v[0] /= len;
v[1] /= len;
v[2] /= len;
end;
function dot(x, y : TFloat3) : Float;
begin
Result := x[0]*y[0] + x[1]*y[1] + x[2]*y[2];
if Result<0 then
Result:=-Result
else Result:=0;
end;
procedure drawSphere(R, k, ambient : Float);
var
vec : TFloat3;
x, y, b : Float;
i, j, size, intensity : Integer;
begin
size:=Trunc(Ceil(R)-Floor(-R)+1);
PrintLn('P2');
PrintLn(IntToStr(size)+' '+IntToStr(size));
PrintLn('255');
for i := Floor(-R) to Ceil(R) do begin
x := i + 0.5;
for j := Floor(-R) to Ceil(R) do begin
y := j + 0.5;
if (x * x + y * y <= R * R) then begin
vec[0] := x;
vec[1] := y;
vec[2] := sqrt(R * R - x * x - y * y);
normalize(vec);
b := Power(dot(light, vec), k) + ambient;
intensity := ClampInt( Round(b*255), 0, 255);
Print(intensity);
Print(' ')
end else Print('0 ');
end;
PrintLn('');
end;
end;
normalize(light);
drawSphere(19, 4, 0.1);
Emacs Lisp
; Draw a sphere
(defun normalize (v)
"Normalize a vector."
(setq invlen (/ 1.0 (sqrt (dot v v))))
(mapcar (lambda (x) (* invlen x)) v))
(defun dot (v1 v2)
"Dot product of two vectors."
(+ (* (car v1) (car v2))
(* (cadr v1) (cadr v2))
(* (caddr v1) (caddr v2))))
(defun make-array (size)
"Create an empty array with size*size elements."
(setq m-array (make-vector size nil))
(dotimes (i size)
(setf (aref m-array i) (make-vector size 0)))
m-array)
(defun pic-lines (arr size)
"Turn array into a string."
(setq all "")
(dotimes (y size)
(setq line "")
(dotimes (x size)
(setq line (concat line (format "%i \n" (elt (elt arr y) x)))))
(setq all (concat all line "\n")))
all)
(defun pic-show (arr size)
"Convert size*size array to grayscale PBM image and show it."
(insert-image (create-image (concat (format "P2
%i %i 255\n" size size) (pic-lines arr size)) 'pbm t)))
(defun sphere (size k amb dir)
"Draw a sphere."
(let ((arr (make-array size))
(ndir (normalize dir))
(r (/ size 2)))
(dotimes (yp size)
(dotimes (xp size)
(setq x (- xp r))
(setq y (- yp r))
(setq z (- (* r r) (* x x) (* y y)))
(if (>= z 0)
(let* ((vec (normalize (list x y (sqrt z))))
(s (max 0 (dot vec ndir)))
(lum (max 0 (min 255 (* 255 (+ amb (expt s k))
(/ (1+ amb)))))))
(setf (elt (elt arr yp) xp) lum)))))
(pic-show arr size)))
(sphere 200 1.5 0.2 '(-30 -30 50))
ERRE
Using ASCII art: output is written to 'SPHERE.PRN' sequential file.
PROGRAM SPHERE
CONST SHADES$=".:!*oe&#%@"
DIM LIGHT[2],X[2],Y[2],V[2],VEC[2]
PROCEDURE DOT(X[],Y[]->D)
D=X[0]*Y[0]+X[1]*Y[1]+X[2]*Y[2]
IF D<0 THEN D=-D ELSE D=0 END IF
END PROCEDURE
PROCEDURE NORMALIZE(V[]->V[])
LUNG=SQR(V[0]*V[0]+V[1]*V[1]+V[2]*V[2])
V[0]=V[0]/LUNG
V[1]=V[1]/LUNG
V[2]=V[2]/LUNG
END PROCEDURE
PROCEDURE PDRAW(R,K,AMBIENT)
FOR I=INT(-R) TO INT(R) DO
X=I+0.5
FOR J=INT(-2*R) TO INT(2*R) DO
Y=J/2+0.5
IF (X*X+Y*Y<=R*R) THEN
VEC[0]=X
VEC[1]=Y
VEC[2]=SQR(R*R-X*X-Y*Y)
NORMALIZE(VEC[]->VEC[])
DOT(LIGHT[],VEC[]->D)
B=D^K+AMBIENT
INTENSITY%=(1-B)*(LEN(SHADES$)-1)
IF (INTENSITY%<0) THEN INTENSITY%=0 END IF
IF (INTENSITY%>=LEN(SHADES$)-1) THEN
INTENSITY%=LEN(SHADES$)-2
END IF
PRINT(#1,MID$(SHADES$,INTENSITY%+1,1);)
ELSE
PRINT(#1,(" ");)
END IF
END FOR
PRINT(#1,)
END FOR
END PROCEDURE
BEGIN
LIGHT[]=(30,30,-50)
OPEN("O",1,"SPHERE.PRN")
NORMALIZE(LIGHT[]->LIGHT[])
PDRAW(10,2,0.4)
PRINT(#1,STRING$(79,"="))
PDRAW(20,4,0.1)
CLOSE(1)
END PROGRAM- Output:
!::::::!!!**o
............:::!!**oe
:................::!!**ooee
:...................::!!**ooeee
......................::!!**ooeee
.......................::!!**ooeeee
.......................:::!!**ooeeeee
:.......................::!!***ooeeeeee
:......................::!!!**oooeeeeee
:....................:::!!!**oooeeeeeee
!:..................:::!!***oooeeeeeeee
!!:..............::::!!!***oooeeeeeeeee
*!!::::.....::::::!!!!***ooooeeeeeeeeee
o*!!!!::::::!!!!!!****ooooeeeeeeeeeee
o****!!!!!!!******oooooeeeeeeeeeeee
eooo********oooooooeeeeeeeeeeeeee
eeeoooooooooooeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
===============================================================================
##############%%%
#&&eeeeeeeeeee&&&&&&######%%%%%
&eeeoooooooooooooeeeee&&&&&######%%%%%%
&eooo**************oooooeeee&&&&&#####%%%%%%%
&eoo**!!!!!!!!!!!!!!*****ooooeeee&&&&######%%%%%%%%
eoo**!!!::::::::::::!!!!****ooooeeee&&&&######%%%%%%%%%
eoo*!!!::::.......::::::!!!!****oooeeee&&&&######%%%%%%%%%%
&eo*!!:::..............::::!!!!***ooooeeee&&&&######%%%%%%%%%%%
eo**!!::.................::::!!!****oooeeee&&&&######%%%%%%%%%%%%
&eo*!!:::..................::::!!!!***oooeeee&&&&&######%%%%%%%%%%%%%
&eo*!!:::...................::::!!!!***oooeeee&&&&&######%%%%%%%%%%%%%%
&eo**!!::....................::::!!!****oooeeee&&&&&######%%%%%%%%%%%%%%%
#eoo*!!:::...................::::!!!!***ooooeeee&&&&#######%%%%%%%%%%%%%%%%
&eo**!!:::.................:::::!!!!****oooeeee&&&&&#######%%%%%%%%%%%%%%%%
&eoo**!!::::...............:::::!!!!****ooooeeee&&&&#######%%%%%%%%%%%%%%%%%%
&eoo**!!!::::...........::::::!!!!*****ooooeeee&&&&&#######%%%%%%%%%%%%%%%%%%
#&eoo***!!!::::::::::::::::::!!!!!****ooooeeeee&&&&&#######%%%%%%%%%%%%%%%%%%%%
#&eeoo***!!!!::::::::::::!!!!!!!*****ooooeeeee&&&&&#######%%%%%%%%%%%%%%%%%%%%%
#&eeooo****!!!!!!!!!!!!!!!!!!******ooooeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%
#&&eeooo******!!!!!!!!!!!*******ooooooeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%%
#&&&eeooooo******************ooooooeeeeee&&&&&&########%%%%%%%%%%%%%%%%%%%%%%%%
##&&&eeeooooooo********oooooooooeeeeeee&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%
###&&&eeeeeooooooooooooooooooeeeeeee&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%%
%###&&&&eeeeeeeeeeeoeeeeeeeeeeeee&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%####&&&&&eeeeeeeeeeeeeeeeee&&&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#####&&&&&&&&&&&&&&&&&&&&&&&&&&&############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######&&&&&&&&&&&&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%############&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%##############################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%#######################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
Evaldraw
Draw a sphere. We dont need to wrap the main () function with braces if we have no functions.
()
cls(0);
clz(1e32);
setcam(0,0,-5,0,0);
setcol(128,64,64);
drawsph(0,0,0,1);
Factor
USING: classes.struct kernel raylib.ffi ;
640 480 "sphere" init-window
S{ Camera3D
{ position S{ Vector3 f 4.5 4.5 4.5 } }
{ target S{ Vector3 f 0 0 0 } }
{ up S{ Vector3 f 0 1 0 } }
{ fovy 45.0 }
{ type 0 }
}
60 set-target-fps
[ window-should-close ] [
begin-drawing
BLACK clear-background dup
begin-mode-3d
S{ Vector3 f 0 0 0 } 2 20 20 LIME draw-sphere-wires
end-mode-3d
end-drawing
] until drop close-window
- Output:
![[2]](https://i.imgur.com/FXHkZm6.png){kind=link}
Forth
Inspired by C version but simplified. Traditionaly, Forth use Fixed-Point Arithmetic (here with a 1000 scale). Integer square root function is hand coded.
ASCII output
: 3dup 2 pick 2 pick 2 pick ;
: sqrt ( u -- sqrt ) ( Babylonian method )
dup 2/ ( first square root guess is half )
dup 0= if drop exit then ( sqrt[0]=0, sqrt[1]=1 )
begin dup >r 2dup / r> + 2/ ( stack: square old-guess new-guess )
2dup > while ( as long as guess is decreasing )
nip repeat ( forget old-guess and repeat )
drop nip ;
: normalize ( x1 y1 z1 -- x1' y1' z1' ) ( normalise down to 1000 )
3dup dup * rot dup * rot dup * + + sqrt 1000 / >r ( length )
r@ / rot r@ / rot r> / rot ;
: r2-y2-x2 ( x y r -- z2 ) dup * swap dup * - swap dup * - ;
: shade ( u -- c ) C" @#&eo%*!:. " + c@ ;
: map-to-shade ( u -- u ) 0 shade * 1000 / 1 max 0 shade min ;
: dot-light ( x y z -- i ) ( hard coded light vector z, y, x )
-770 * rot 461 * rot 461 * + +
0 min 1000 / ;
: intensity ( x y z -- u ) dot-light dup * 1000 / map-to-shade ;
: pixel ( x y r -- c )
3dup r2-y2-x2 dup 0> if ( if in disk )
sqrt nip normalize intensity shade ( z=sqrt[r2-x2-y2] )
else 2drop 2drop bl ( else blank )
then ;
: draw ( r -- ) ( r x1000 )
1000 * dup dup negate do
cr
dup dup negate do
dup I 500 + J 500 + rot pixel emit
500 +loop
1000 +loop drop ;
20 draw
10 draw
- Output:
eeooooeeeeee&&&##
o%%%%******%%%%%%ooooeee&&&##@@
o%**!!!!!!!!!!!!*****%%%%oooeee&&&##@@@
%*!!!:::::::::::::!!!!!****%%%oooeee&&&##@@@@
%*!!:::............:::::!!!!****%%%oooeee&&###@@@@@
%*!::...... ........::::!!!!***%%%oooeee&&&##@@@@@@
%!!::... .....::::!!!!***%%%oooeee&&&##@@@@@@@
%*!::... .....::::!!!****%%%oooee&&&###@@@@@@@@
*!::... .....:::!!!!***%%%oooeee&&&###@@@@@@@@
o*!::.. .....::::!!!***%%%oooeee&&&###@@@@@@@@@@
o*!::.. .....::::!!!***%%%oooeee&&&####@@@@@@@@@@
o*!::... ....::::!!!!***%%%oooeee&&&&###@@@@@@@@@@@
o*!!::.. .....::::!!!****%%%oooeee&&&####@@@@@@@@@@@@
%*!::... .....::::!!!!***%%%%oooeee&&&####@@@@@@@@@@@@
o%*!::.... .....::::!!!!****%%%oooeeee&&&###@@@@@@@@@@@@@@
%**!:::.... ......::::!!!!****%%%ooooeee&&&####@@@@@@@@@@@@@@
e%**!!::..... .......:::::!!!!****%%%ooooeee&&&&####@@@@@@@@@@@@@@@
o%**!!::::.....................:::::!!!!*****%%%ooooeee&&&&####@@@@@@@@@@@@@@@@
o%%**!!:::::...............:::::::!!!!!****%%%%ooooeeee&&&####@@@@@@@@@@@@@@@@@
eo%***!!!:::::::......:::::::::!!!!!!****%%%%%ooooeee&&&&####@@@@@@@@@@@@@@@@@@
eo%%***!!!!:::::::::::::::::!!!!!!******%%%%ooooeeee&&&&####@@@@@@@@@@@@@@@@@@@
eeo%%****!!!!!!!!::::!!!!!!!!!!******%%%%%oooooeeee&&&&####@@@@@@@@@@@@@@@@@@@@
&eoo%%%*****!!!!!!!!!!!!!!!********%%%%%oooooeeee&&&&&####@@@@@@@@@@@@@@@@@@@@@
#&eooo%%%%*********************%%%%%%ooooooeeee&&&&&#####@@@@@@@@@@@@@@@@@@@@@@
&&eeooo%%%%%%************%%%%%%%%ooooooeeeee&&&&&#####@@@@@@@@@@@@@@@@@@@@@@@
#&&eeeoooo%%%%%%%%%%%%%%%%%%%oooooooeeeeee&&&&&#####@@@@@@@@@@@@@@@@@@@@@@@@@
##&&eeeeoooooooooooooooooooooooeeeeeee&&&&&&#####@@@@@@@@@@@@@@@@@@@@@@@@@@
@##&&&eeeeeeooooooooooooooeeeeeeeee&&&&&&######@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@##&&&&&eeeeeeeeeeeeeeeeeeee&&&&&&&&#######@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@###&&&&&&&&&&&&&&&&&&&&&&&&&&########@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@######&&&&&&&&&&&&&&&##########@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@#######################@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@########@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@
o%%%%%%ooe&#@
*!::...:::!!*%%oe&&#@
*:. ..::!!*%ooe&#@@@
*: ..:!!*%ooe&#@@@@
!. ..::!*%%oe&&#@@@@
!. ..::!*%%oee&#@@@@@
!: ..:!!*%%oe&&#@@@@@@
%!. ..:!!**%ooe&&#@@@@@@@
%!:. ..::!!**%ooe&&##@@@@@@@
%!::.. ...:::!!*%%ooee&##@@@@@@@@
o*!!::.......:::!!!**%%oee&&##@@@@@@@@@
eo%*!!!!:::!!!!!**%%%ooee&&##@@@@@@@@@@
#eo%%**********%%%ooeee&&##@@@@@@@@@@@@
#&eooo%%%%%%ooooeee&&&###@@@@@@@@@@@@
##&&eeeeeeeeee&&&&###@@@@@@@@@@@@@@
@@##&&&&&&&&#####@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@ ok
PGM output
The same program as the ASCII one is translated to produce a PGM portable pixmap image file.
: 3dup 2 pick 2 pick 2 pick ;
: sqrt ( u -- sqrt ) ( Babylonian method )
dup 2/ ( first square root guess is half )
dup 0= if drop exit then ( sqrt[0]=0, sqrt[1]=1 )
begin dup >r 2dup / r> + 2/ ( stack: square old-guess new-guess )
2dup > while ( as long as guess is decreasing )
nip repeat ( forget old-guess and repeat )
drop nip ;
: normalize ( x1 y1 z1 -- x1' y1' z1' ) ( normalise down to 1000 )
3dup dup * rot dup * rot dup * + + sqrt 1000 / >r ( length )
r@ / rot r@ / rot r> / rot ;
: r2-y2-x2 ( x y r -- z2 ) dup * swap dup * - swap dup * - ;
0 value fileidstore
: image-open ( r -- )
outfile-id to fileidstore
s" sphere.pgm" w/o create-file throw to outfile-id
s\" P2\n" type 2* dup . .
s\" \n255" type ;
: image-close outfile-id close-file throw fileidstore to outfile-id ;
: map-to-shade 255 * 1000 / 1 max 255 min ;
: dot-light ( x y z -- i ) ( hard coded light vector z, y, x )
-770 * rot 461 * rot 461 * + +
0 min 1000 / ;
: intensity ( x y z -- u ) dot-light dup * 1000 / map-to-shade ;
: pixel ( x y r -- c )
3dup r2-y2-x2 dup 0> if ( if in disk )
sqrt nip normalize intensity ( z=sqrt[r2-x2-y2] )
else 2drop 2drop 255 ( else blank )
then ;
: draw ( r -- ) ( r x1000 )
dup image-open
1000 * dup dup negate do
cr
dup dup negate do
dup I 500 + J 500 + rot pixel .
1000 +loop
1000 +loop drop image-close ;
200 draw
Frink
This program not only draws a sphere and renders it onscreen projected on the x,y, and z axes but also outputs a .stl file for 3-D printing or display in a 3-D modeling package like MeshLab! Frink has built-in routines for 3-D modeling and can emit STL files or Wavefront OBJ files natively! Frink will let you print a sphere that you can hold in your hand!
res = 254 / in
v = callJava["frink.graphics.VoxelArray", "makeSphere", [1/2 inch res]]
v.projectX[undef].show["X"]
v.projectY[undef].show["Y"]
v.projectZ[undef].show["Z"]
filename = "sphere.stl"
print["Writing $filename..."]
w = new Writer[filename]
w.println[v.toSTLFormat["sphere", 1/(res mm)]]
w.close[]
println["done."]FutureBasic
_window = 1
begin enum output 1
_sphereImageView
end enum
void local fn BuildWindow
CGRect r = fn CGRectMake( 0, 0, 400, 400 )
window _window, @"Rosetta Code Sphere", r, NSWindowStyleMaskTitled + NSWindowStyleMaskClosable
r = fn CGRectMake( 20, 20, 360, 360 )
imageview _sphereImageView, YES, , r, NSImageScaleAxesIndependently, NSImageAlignCenter, NSImageFrameNone, _window
end fn
local fn SphereImageWithCIFilter( imageDimension as NSUInteger, sphereColor as ColorRef, backgroundColor as ColorRef, radiusBlur as float, radiusSphere as float ) as ImageRef
CIVectorRef civ = fn CIVectorWithXY( imageDimension/2, imageDimension/2 )
CIFilterRef filter = fn CIFilterWithName( @"CIRadialGradient" )
CIFilterSetDefaults( filter )
ObjectSetValueForKey( filter, civ, @"inputCenter" )
ObjectSetValueForKey( filter, fn NumberWithFloat( radiusBlur ), @"inputRadius0" )
ObjectSetValueForKey( filter, fn NumberWithFloat( radiusSphere ), @"inputRadius1" )
ObjectSetValueForKey( filter, fn CIColorWithCGColor( fn ColorCGColor( sphereColor ) ), @"inputColor0" )
ObjectSetValueForKey( filter, fn CIColorWithCGColor( fn ColorCGColor( backgroundColor ) ), @"inputColor1" )
ImageRef resultImage = fn ImageWithSize( fn CGSizeMake( imageDimension, imageDimension ) )
ImageLockFocus( resultImage )
CIImageDrawAtPoint( fn CIFilterOutputImage( filter ), CGPointZero, fn CGRectMake( 0, 0, imageDimension, imageDimension ), NSCompositeDestinationAtop, 1.0 )
ImageUnlockFocus( resultImage )
end fn = resultImage
local fn BuildSphere
ImageRef sphereImage = fn SphereImageWithCIFilter( 340, fn ColorWithRGB( 0.988, 0.335, 0.176, 1.0 ), fn ColorBlack, 0.0, 125.0 )
ImageViewSetImage( _sphereImageView, sphereImage )
end fn
fn BuildWindow
fn BuildSphere
HandleEvents- Output:
Go
Using image library rather than ASCII art.
package main
import (
"fmt"
"image"
"image/color"
"image/png"
"math"
"os"
)
type vector [3]float64
func normalize(v *vector) {
invLen := 1 / math.Sqrt(dot(v, v))
v[0] *= invLen
v[1] *= invLen
v[2] *= invLen
}
func dot(x, y *vector) float64 {
return x[0]*y[0] + x[1]*y[1] + x[2]*y[2]
}
func drawSphere(r int, k, amb float64, dir *vector) *image.Gray {
w, h := r*4, r*3
img := image.NewGray(image.Rect(-w/2, -h/2, w/2, h/2))
vec := new(vector)
for x := -r; x < r; x++ {
for y := -r; y < r; y++ {
if z := r*r - x*x - y*y; z >= 0 {
vec[0] = float64(x)
vec[1] = float64(y)
vec[2] = math.Sqrt(float64(z))
normalize(vec)
s := dot(dir, vec)
if s < 0 {
s = 0
}
lum := 255 * (math.Pow(s, k) + amb) / (1 + amb)
if lum < 0 {
lum = 0
} else if lum > 255 {
lum = 255
}
img.SetGray(x, y, color.Gray{uint8(lum)})
}
}
}
return img
}
func main() {
dir := &vector{-30, -30, 50}
normalize(dir)
img := drawSphere(200, 1.5, .2, dir)
f, err := os.Create("sphere.png")
if err != nil {
fmt.Println(err)
return
}
if err = png.Encode(f, img); err != nil {
fmt.Println(err)
}
if err = f.Close(); err != nil {
fmt.Println(err)
}
}
Haskell
import Graphics.Rendering.OpenGL.GL
import Graphics.UI.GLUT.Objects
import Graphics.UI.GLUT
setProjection :: IO ()
setProjection = do
matrixMode $= Projection
ortho (-1) 1 (-1) 1 0 (-1)
grey1,grey9,red,white :: Color4 GLfloat
grey1 = Color4 0.1 0.1 0.1 1
grey9 = Color4 0.9 0.9 0.9 1
red = Color4 1 0 0 1
white = Color4 1 1 1 1
setLights :: IO ()
setLights = do
let l = Light 0
ambient l $= grey1
diffuse l $= white
specular l $= white
position l $= Vertex4 (-4) 4 3 (0 :: GLfloat)
light l $= Enabled
lighting $= Enabled
setMaterial :: IO ()
setMaterial = do
materialAmbient Front $= grey1
materialDiffuse Front $= red
materialSpecular Front $= grey9
materialShininess Front $= (32 :: GLfloat)
display :: IO()
display = do
clear [ColorBuffer]
renderObject Solid $ Sphere' 0.8 64 64
swapBuffers
main :: IO()
main = do
_ <- getArgsAndInitialize
_ <- createWindow "Sphere"
clearColor $= Color4 0.0 0.0 0.0 0.0
setProjection
setLights
setMaterial
displayCallback $= display
mainLoop
ASCII art
import Data.List (genericLength)
shades = ".:!*oe%#&@"
n = genericLength shades
dot a b = sum $ zipWith (*) a b
normalize x = (/ sqrt (x `dot` x)) <$> x
sphere r k amb light = unlines $
[ [ if x*x + y*y <= r*r
then let vec = normalize [x, y, sqrt (r*r-x*x-y*y)]
b = (light `dot` vec) ** k + amb
intensity = (1 - b)*(n - 1)
in shades !! round ((0 `max` intensity) `min` n)
else ' '
| y <- map (/2.12) [- 2*r - 0.5 .. 2*r + 0.5] ]
| x <- [ - r - 0.5 .. r + 0.5] ]
λ> putStrLn $ sphere 10 4 0.1 (normalize [30,30,-50])
#%%%%%%%####&&
eoo*****oooee%%%###&&&
eo*!!::::!!!**ooee%%%###&&&&
e*!::......::!!**ooee%%####&&&&&
%o!::.........::!!**ooee%%###&&&&&&&
eo!::..........::!!**ooee%%###&&&&&&&&
%o*!:..........::!!**ooee%%%###&&&&&&&&&
#eo*!::.......:::!!**ooeee%%####&&&&&&&&&&
%eo*!!:::::::::!!***ooeee%%####&&&&&&&&&&&
%eeo**!!!!!!!!****ooeee%%%####&&&&&&&&&&&&
#%eeooo*******ooooeee%%%%####&&&&&&&&&&&&&
##%%eeeoooooooeeeee%%%%####&&&&&&&&&&&&&&&
&###%%%%eeeeee%%%%%%######&&&&&&&&&&&&&&&#
&&####%%%%%%%%########&&&&&&&&&&&&&&&&&&
&&&##############&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&#
Icon and Unicon
Unicon provides a built-in interface to openGL including some higher level abstractions (for more information see Unicon Technical References, 3D Graphics). The example below draws a blue sphere on a black background and waits for input to quit.
procedure main()
W := open("Demo", "gl", "size=400,400", "bg=black") | stop("can't open window!")
WAttrib(W, "slices=40", "rings=40", "light0=on, ambient white; diffuse gold; specular gold; position 5, 0, 0" )
Fg(W, "emission blue")
DrawSphere(W, 0, 0, -5, 1)
Event(W)
end
J
Demo Solution
The simplest way to draw a sphere is to run the sphere demo code from J's simple demos. (This assumes J version 6.)
Normally you would bring up this demo by using the menu system:
Studio
> Demos...
> opengl simple... [ok]
> sphere [Run]
But bringing up the example with a line of code is trivial enough:
load '~system/examples/graphics/opengl/simple/sphere.ijs'
(Note that this example has been removed from recent versions of J, but still works for J version 5 and version 6.)
Raytracing Solution
Here's a version using raytracing computed in J. luminosity is an array of luminosity values with theoretical maximum 1 and minimum 0, and viewmat is used to display this.
'R k ambient' =. 10 2 0.4
light =. (% +/&.:*:) 30 30 _50
pts =. (0&*^:(0={:))@:(,,(0>.(*:R)-+)&.*:)"0/~ i:15j200
luminosity =. (>:ambient) %~ (ambient * * +/&.:*:"1 pts) + k^~ 0>. R%~ pts +/@:*"1 -light
load 'viewmat'
torgb =. 256 #. [: <. 255 255 255 *"1 0 ]
'rgb' viewmat torgb luminosity
Java
public class Sphere{
static char[] shades = {'.', ':', '!', '*', 'o', 'e', '&', '#', '%', '@'};
static double[] light = { 30, 30, -50 };
private static void normalize(double[] v){
double len = Math.sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
v[0] /= len; v[1] /= len; v[2] /= len;
}
private static double dot(double[] x, double[] y){
double d = x[0]*y[0] + x[1]*y[1] + x[2]*y[2];
return d < 0 ? -d : 0;
}
public static void drawSphere(double R, double k, double ambient){
double[] vec = new double[3];
for(int i = (int)Math.floor(-R); i <= (int)Math.ceil(R); i++){
double x = i + .5;
for(int j = (int)Math.floor(-2 * R); j <= (int)Math.ceil(2 * R); j++){
double y = j / 2. + .5;
if(x * x + y * y <= R * R) {
vec[0] = x;
vec[1] = y;
vec[2] = Math.sqrt(R * R - x * x - y * y);
normalize(vec);
double b = Math.pow(dot(light, vec), k) + ambient;
int intensity = (b <= 0) ?
shades.length - 2 :
(int)Math.max((1 - b) * (shades.length - 1), 0);
System.out.print(shades[intensity]);
} else
System.out.print(' ');
}
System.out.println();
}
}
public static void main(String[] args){
normalize(light);
drawSphere(20, 4, .1);
drawSphere(10, 2, .4);
}
}
- Output:
&&&&&&&&&&#######
&eeeeeeeeeeeeeeee&&&&&&#######%
&eoooo*******oooooooeeeee&&&&&########%
eoo****!!!!!!!!******oooooeeee&&&&&########%%
eoo**!!!!::::::::!!!!!*****ooooeeee&&&&&########%%%
eo**!!::::::...:::::::!!!!!***ooooeeee&&&&&########%%%%
eo*!!:::.............:::::!!!!***ooooeeee&&&&&########%%%%%
eo*!!:::.................::::!!!!***ooooeeee&&&&#########%%%%%%
eo*!!::....................::::!!!****oooeeee&&&&&#########%%%%%%
&o**!::......................::::!!!****oooeeee&&&&&##########%%%%%%%
&o**!::.......................::::!!!****oooeeee&&&&&##########%%%%%%%%
&oo*!!::.......................:::!!!!***ooooeeee&&&&&##########%%%%%%%%%
&eo*!!::.......................::::!!!****ooooeeee&&&&&##########%%%%%%%%%%
eo**!!::......................::::!!!!***ooooeeeee&&&&&##########%%%%%%%%%%
&eo**!!:::...................:::::!!!!****ooooeeee&&&&&###########%%%%%%%%%%%
eeo**!!::::................:::::!!!!!****ooooeeee&&&&&&###########%%%%%%%%%%%
&eeo***!!:::::...........::::::!!!!!****oooooeeee&&&&&&###########%%%%%%%%%%%%%
&eeoo**!!!!::::::::::::::::::!!!!!*****ooooeeeee&&&&&&############%%%%%%%%%%%%%
&eeooo***!!!!::::::::::::!!!!!!!*****oooooeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeooo***!!!!!!!!!!!!!!!!!!!******oooooeeeeee&&&&&&############%%%%%%%%%%%%%%%
&&eeeooo******!!!!!!!!!!********ooooooeeeeee&&&&&&&############%%%%%%%%%%%%%%%%
#&&eeeooooo******************oooooooeeeeee&&&&&&&#############%%%%%%%%%%%%%%%%%
#&&&eeeeoooooooo******oooooooooooeeeeeee&&&&&&&&#############%%%%%%%%%%%%%%%%%%
##&&&&eeeeeooooooooooooooooooeeeeeeee&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%
##&&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&################%%%%%%%%%%%%%%%%%%%
####&&&&&&eeeeeeeeeeeeeeeeeee&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%%
#####&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#################%%%%%%%%%%%%%%%%%%%%%%
%#######&&&&&&&&&&&&&&&&&&&&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%
%###########&&&&&&&&&&&&&#######################%%%%%%%%%%%%%%%%%%%%%%%%%
%############################################%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%#########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%#############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::...:::!!!*o
..............::!!*oo
..................::!!**ooe
.....................::!!**ooee
.......................::!!**ooee
........................::!!**oooee
.........................::!!**oooeee
:........................::!!!**oooeeee
........................::!!!**ooooeeee
:......................::!!!***oooeeeee
:....................:::!!!***oooeeeeee
!:.................:::!!!****oooeeeeeee
*!:::...........::::!!!!***ooooeeeeeeee
*!!!:::::::::::!!!!!****oooooeeeeeeee
o**!!!!!!!!!!!!!*****oooooeeeeeeeee
oo**************ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
JavaScript
This Javascript entry uses an HTML wrapper to offer easy running and some interactivity. It is made as such, though, that the entire HTML wrapper can be removed (except for a canvas with id c) and still work. If you remove the HTML, call the draw_sphere function to draw the thing.
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<title>Draw a sphere</title>
<script>
var light=[30,30,-50],gR,gk,gambient;
function normalize(v){
var len=Math.sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]);
v[0]/=len;
v[1]/=len;
v[2]/=len;
return v;
}
function dot(x,y){
var d=x[0]*y[0]+x[1]*y[1]+x[2]*y[2];
return d<0?-d:0;
}
function draw_sphere(R,k,ambient){
var i,j,intensity,b,vec,x,y,cvs,ctx,imgdata,idx;
cvs=document.getElementById("c");
ctx=cvs.getContext("2d");
cvs.width=cvs.height=2*Math.ceil(R)+1;
imgdata=ctx.createImageData(2*Math.ceil(R)+1,2*Math.ceil(R)+1);
idx=0;
for(i=Math.floor(-R);i<=Math.ceil(R);i++){
x=i+.5;
for(j=Math.floor(-R);j<=Math.ceil(R);j++){
y=j+.5;
if(x*x+y*y<=R*R){
vec=[x,y,Math.sqrt(R*R-x*x-y*y)];
vec=normalize(vec);
b=Math.pow(dot(light,vec),k)+ambient;
intensity=(1-b)*256;
if(intensity<0)intensity=0;
if(intensity>=256)intensity=255;
imgdata.data[idx++]=imgdata.data[idx++]=255-~~(intensity); //RG
imgdata.data[idx++]=imgdata.data[idx++]=255; //BA
} else {
imgdata.data[idx++]=imgdata.data[idx++]=imgdata.data[idx++]=imgdata.data[idx++]=255; //RGBA
}
}
}
ctx.putImageData(imgdata,0,0);
}
light=normalize(light);
</script>
</head>
<body onload="gR=200;gk=4;gambient=.2;draw_sphere(gR,gk,gambient)">
R=<input type="range" id="R" name="R" min="5" max="500" value="200" step="5" onchange="document.getElementById('lR').innerHTML=gR=parseFloat(this.value);draw_sphere(gR,gk,gambient)">
<label for="R" id="lR">200</label><br>
k=<input type="range" id="k" name="k" min="0" max="10" value="4" step=".25" onchange="document.getElementById('lk').innerHTML=gk=parseFloat(this.value);draw_sphere(gR,gk,gambient)">
<label for="k" id="lk">4</label><br>
ambient=<input type="range" id="ambient" name="ambient" min="0" max="1" value=".2" step=".05" onchange="document.getElementById('lambient').innerHTML=gambient=parseFloat(this.value);draw_sphere(gR,gk,gambient)">
<label for="ambient" id="lambient">0.2</label><br>
<canvas id="c">Unsupportive browser...</canvas><br>
</body>
</html>
jq
The approach adopted here is to generate an SVG file, which may then be viewed, for example, in a web browser.
def svg:
"<svg width='100%' height='100%' version='1.1'
xmlns='http://www.w3.org/2000/svg'
xmlns:xlink='http://www.w3.org/1999/xlink'>" ;
# A radial gradient to make a circle look like a sphere.
# "colors" should be [startColor, intermediateColor, endColor]
# or null for ["white", "teal", "black"]
def sphericalGradient(id; colors):
"<defs>
<radialGradient id = '\(id)' cx = '30%' cy = '30%' r = '100%' fx='10%' fy='10%' >
<stop stop-color = '\(colors[0]//"white")' offset = '0%'/>
<stop stop-color = '\(colors[1]//"teal")' offset = '50%'/>
<stop stop-color = '\(colors[1]//"black")' offset = '100%'/>
</radialGradient>
</defs>" ;
def sphere(cx; cy; r; gradientId):
"<circle fill='url(#\(gradientId))' cx='\(cx)' cy='\(cy)' r='\(r)' />" ;Example:
def draw_sphere:
svg,
"<title>Teal sphere</title>",
sphericalGradient("tealGradient"; null), # define the gradient to use
sphere(100;100;100; "tealGradient"), # draw a sphere using the gradient
sphere(100;300;100; "tealGradient"), # draw another sphere using the same gradient
"</svg>" ;
draw_sphere- Output:
$ jq -r -n -f spheres.jq > spheres.svg
One way to view the output as an image is to point your browser to the generated SVG.
Julia
ASCII Text
function draw_sphere(r, k, ambient, light)
shades = ('.', ':', '!', '*', 'o', 'e', '&', '#', '%', '@')
for i in floor(Int, -r):ceil(Int, r)
x = i + 0.5
line = IOBuffer()
for j in floor(Int, -2r):ceil(2r)
y = j / 2 + 0.5
if x ^ 2 + y ^ 2 ≤ r ^ 2
v = normalize([x, y, sqrt(r ^ 2 - x ^ 2 - y ^ 2)])
b = dot(light, v) ^ k + ambient
intensity = ceil(Int, (1 - b) * (length(shades) - 1))
if intensity < 1
intensity = 1 end
if intensity > length(shades)
intensity = length(shades) end
print(shades[intensity])
else
print(' ')
end
end
println()
end
end
light = normalize([30, 30, -50])
draw_sphere(20, 4, 0.1, light)
draw_sphere(10, 2, 0.4, light)
Graphical
# run from REPL
using Makie
φ = 0:π/100:2π
θ = 0:π/200:π
x = [cos(θ) * sin(φ) for θ in θ, φ in φ]
y = [sin(θ)*sin(φ) for θ in θ, φ in φ]
z = [cos(φ) for θ in θ, φ in φ]
surface(x, y, z, backgroundcolor = :black, show_axis = false)
Kotlin
// version 1.0.6
const val shades = ".:!*oe&#%@"
val light = doubleArrayOf(30.0, 30.0, -50.0)
fun normalize(v: DoubleArray) {
val len = Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2])
v[0] /= len; v[1] /= len; v[2] /= len
}
fun dot(x: DoubleArray, y: DoubleArray): Double {
val d = x[0] * y[0] + x[1] * y[1] + x[2] * y[2]
return if (d < 0.0) -d else 0.0
}
fun drawSphere(r: Double, k: Double, ambient: Double) {
val vec = DoubleArray(3)
var intensity: Int
var b : Double
var x: Double
var y: Double
for (i in Math.floor(-r).toInt() .. Math.ceil(r).toInt()) {
x = i + 0.5
for (j in Math.floor(-2.0 * r).toInt() .. Math.ceil(2.0 * r).toInt()) {
y = j / 2.0 + 0.5
if (x * x + y * y <= r * r) {
vec[0] = x
vec[1] = y
vec[2] = Math.sqrt(r * r - x * x - y * y)
normalize(vec)
b = Math.pow(dot(light, vec), k) + ambient
intensity = ((1.0 - b) * (shades.length - 1)).toInt()
if (intensity < 0) intensity = 0
if (intensity >= shades.length - 1) intensity = shades.length - 2
print(shades[intensity])
}
else print(' ')
}
println()
}
}
fun main(args: Array<String>) {
normalize(light)
drawSphere(20.0, 4.0, 0.1)
drawSphere(10.0, 2.0, 0.4)
}
- Output:
&&&&&&&&&&#######
&eeeeeeeeeeeeeeee&&&&&&#######%
&eoooo*******oooooooeeeee&&&&&########%
eoo****!!!!!!!!******oooooeeee&&&&&########%%
eoo**!!!!::::::::!!!!!*****ooooeeee&&&&&########%%%
eo**!!::::::...:::::::!!!!!***ooooeeee&&&&&########%%%%
eo*!!:::.............:::::!!!!***ooooeeee&&&&&########%%%%%
eo*!!:::.................::::!!!!***ooooeeee&&&&#########%%%%%%
eo*!!::....................::::!!!****oooeeee&&&&&#########%%%%%%
&o**!::......................::::!!!****oooeeee&&&&&##########%%%%%%%
&o**!::.......................::::!!!****oooeeee&&&&&##########%%%%%%%%
&oo*!!::.......................:::!!!!***ooooeeee&&&&&##########%%%%%%%%%
&eo*!!::.......................::::!!!****ooooeeee&&&&&##########%%%%%%%%%%
eo**!!::......................::::!!!!***ooooeeeee&&&&&##########%%%%%%%%%%
&eo**!!:::...................:::::!!!!****ooooeeee&&&&&###########%%%%%%%%%%%
eeo**!!::::................:::::!!!!!****ooooeeee&&&&&&###########%%%%%%%%%%%
&eeo***!!:::::...........::::::!!!!!****oooooeeee&&&&&&###########%%%%%%%%%%%%%
&eeoo**!!!!::::::::::::::::::!!!!!*****ooooeeeee&&&&&&############%%%%%%%%%%%%%
&eeooo***!!!!::::::::::::!!!!!!!*****oooooeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeooo***!!!!!!!!!!!!!!!!!!!******oooooeeeeee&&&&&&############%%%%%%%%%%%%%%%
&&eeeooo******!!!!!!!!!!********ooooooeeeeee&&&&&&&############%%%%%%%%%%%%%%%%
#&&eeeooooo******************oooooooeeeeee&&&&&&&#############%%%%%%%%%%%%%%%%%
#&&&eeeeoooooooo******oooooooooooeeeeeee&&&&&&&&#############%%%%%%%%%%%%%%%%%%
##&&&&eeeeeooooooooooooooooooeeeeeeee&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%
##&&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&################%%%%%%%%%%%%%%%%%%%
####&&&&&&eeeeeeeeeeeeeeeeeee&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%%
#####&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#################%%%%%%%%%%%%%%%%%%%%%%
%#######&&&&&&&&&&&&&&&&&&&&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%
%###########&&&&&&&&&&&&&#######################%%%%%%%%%%%%%%%%%%%%%%%%%
%############################################%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%#########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%#############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::...:::!!!*o
..............::!!*oo
..................::!!**ooe
.....................::!!**ooee
.......................::!!**ooee
........................::!!**oooee
.........................::!!**oooeee
:........................::!!!**oooeeee
........................::!!!**ooooeeee
:......................::!!!***oooeeeee
:....................:::!!!***oooeeeeee
!:.................:::!!!****oooeeeeeee
*!:::...........::::!!!!***ooooeeeeeeee
*!!!:::::::::::!!!!!****oooooeeeeeeee
o**!!!!!!!!!!!!!*****oooooeeeeeeeee
oo**************ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
Lingo
----------------------------------------
-- Draw a circle
-- @param {image} img
-- @param {integer} x
-- @param {integer} y
-- @param {integer} r
-- @param {integer} lineSize
-- @param {color} drawColor
----------------------------------------
on circle (img, x, y, r, lineSize, drawColor)
props = [:]
props[#shapeType] = #oval
props[#lineSize] = lineSize
props[#color] = drawColor
img.draw(x-r, y-r, x+r, y+r, props)
endLogo
Drawing a sphere is actually very simple in logo, using the perspective function to make life easier.
to sphere :r
cs perspective ht ;making the room ready to use
repeat 180 [polystart circle :r polyend down 1]
polyview
endLua
require ("math")
shades = {'.', ':', '!', '*', 'o', 'e', '&', '#', '%', '@'}
function normalize (vec)
len = math.sqrt(vec[1]^2 + vec[2]^2 + vec[3]^2)
return {vec[1]/len, vec[2]/len, vec[3]/len}
end
light = normalize{30, 30, -50}
function dot (vec1, vec2)
d = vec1[1]*vec2[1] + vec1[2]*vec2[2] + vec1[3]*vec2[3]
return d < 0 and -d or 0
end
function draw_sphere (radius, k, ambient)
for i = math.floor(-radius),-math.floor(-radius) do
x = i + .5
local line = ''
for j = math.floor(-2*radius),-math.floor(-2*radius) do
y = j / 2 + .5
if x^2 + y^2 <= radius^2 then
vec = normalize{x, y, math.sqrt(radius^2 - x^2 - y^2)}
b = dot(light,vec) ^ k + ambient
intensity = math.floor ((1 - b) * #shades)
line = line .. (shades[intensity] or shades[1])
else
line = line .. ' '
end
end
print (line)
end
end
draw_sphere (20, 4, 0.1)
draw_sphere (10, 2, 0.4)
- Output:
&&&&&&&&&&&&#####
&eeeoooooooooeeeeee&&&&&#######
eooo*************oooooeeee&&&&&########
eo**!!!!!!!!!!!!!!!*****ooooeeee&&&&#########
eo*!!!:::::...:::::::!!!!****oooeeee&&&&&##########
o**!:::..............::::!!!!***ooooeee&&&&&###########
o*!!::...................::::!!!***ooooeee&&&&&############
eo*!::......................::::!!!***oooeeee&&&&&#############
o*!::.........................:::!!!***ooooeee&&&&&##############
&o*!::..........................:::!!!***ooooeeee&&&&###############%
eo*!::...........................:::!!!***ooooeeee&&&&&###############%
eo*!::............................:::!!!***ooooeeee&&&&&###############%%
&o*!!::...........................:::!!!!***oooeeee&&&&&#################%%
eo*!!:...........................::::!!!***ooooeeee&&&&&#################%%
eo**!!::.........................::::!!!****oooeeee&&&&&&#################%%%
eo**!!::.......................::::!!!!****oooeeeee&&&&&##################%%%
&eo**!!:::....................:::::!!!!***ooooeeeee&&&&&&##################%%%%
&eoo**!!::::................:::::!!!!****ooooeeeee&&&&&&###################%%%%
&eoo***!!!:::::........:::::::!!!!!****oooooeeeee&&&&&&###################%%%%%
&eeoo***!!!!:::::::::::::::!!!!!!*****ooooeeeee&&&&&&&####################%%%%%
&&eeoo****!!!!!!!!!!!!!!!!!!!!*****oooooeeeeee&&&&&&######################%%%%%
&&eeeooo******!!!!!!!!!!!*******ooooooeeeeee&&&&&&&######################%%%%%%
#&&eeeooooo******************oooooooeeeeee&&&&&&&#######################%%%%%%%
##&&&eeeeoooooooooo*ooooooooooooeeeeeeee&&&&&&&&#######################%%%%%%%%
##&&&eeeeeeooooooooooooooooeeeeeeeee&&&&&&&&&########################%%%%%%%%
###&&&&&eeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&&##########################%%%%%%%%%
####&&&&&&&eeeeeeeeeeeeeee&&&&&&&&&&&&############################%%%%%%%%%
######&&&&&&&&&&&&&&&&&&&&&&&&&&&&&##############################%%%%%%%%%%
########&&&&&&&&&&&&&&&&&&&&&&################################%%%%%%%%%%%
###############&&&&&#######################################%%%%%%%%%%%%
#########################################################%%%%%%%%%%%%
#####################################################%%%%%%%%%%%%
#################################################%%%%%%%%%%%%%%
#############################################%%%%%%%%%%%%%%
########################################%%%%%%%%%%%%%%%
##################################%%%%%%%%%%%%%%%%%
%##########################%%%%%%%%%%%%%%%%%%
%%%%############%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
........::!!*
...............::!!*o
....................::!**oo
.......................::!**ooo
........................::!!**ooo
.........................::!!**oooo
..........................::!!**ooooe
...........................::!!**ooooee
..........................::!!***ooooee
.........................::!!!**oooooee
.......................:::!!!**oooooeee
:.....................::!!!***ooooooeee
!::................:::!!!!***ooooooeeee
!!::..........:::::!!!****ooooooeeeee
*!!!::::::::::!!!!!****oooooooeeeee
o***!!!!!!!!!******ooooooooeeeeee
ooo***********ooooooooooeeeeeee
oooooooooooooooooooeeeeeeee
eooooooooooeeeeeeeeee
eeeeeeeeeeeee
M2000 Interpreter
Module CheckIt {
Er$="Pset is a new statement"
If Version<9.4 Then Error Er$
If Version=9.4 then If revision<26 then Error Er$
Form 60, 40
Cls 0 ' Black
Gradient 0,1
Pen 14 ' Yellow
Set Fast !
Refresh 500
Module Sphere (R as long, X0 as long, Y0 as long, fun){
R2 = R * R
Def Long X, Y, D2
Let Scale=twipsx/R*13.5
For Y = -R To R step twipsx {
Move X0-R, Y+Y0
For X = -R To R step twipsy {
D2 = X **2 + Y **2
IF R2>D2 THEN Pset Fun(Max.Data(Min.Data((Sqrt(R2 - D2) - ( X + Y) / 2 )*Scale ,255),0))
Step twipsx
}
}
}
Blue=lambda (c)->{
c1=c/4+192
=Color(c,c,c1)
}
Blue1=lambda (c)->{
c1=c/4+Random(150,192)
=Color(c,c,c1)
}
Mystery=lambda m=1 (c)->{
c1=c/4+m
m+=10
if m>192 then m=1
=Color(c,c,c1)
}
Mystery2=lambda m=1, p=true (c)->{
c1=c/4+m
if p then m+=10
Else m=-10
if m>192 then m-=10 : p=false
If m<0 then m+=10: p=true
=Color(c,c,c1)
}
Buffer Alfa as byte*8
Trans =lambda Alfa (c) -> {
Return Alfa, 0:=-point as long
Return Alfa, 4:=-color(c,c, c/4+192) as long
for i=0 to 2: Return Alfa, i:=(Eval(Alfa, i)+Eval(Alfa, i+4))/2: Next i
=-Eval(Alfa, 0 as long)
}
Sphere 2400, 9000,7000, Blue
Sphere 800, 6000, 7000, Blue1
Sphere 1200, 5000,5000, Mystery
Sphere 1200, 10000,6000, Mystery2
Sphere 1200, 8000,5000, trans
}
Checkit[[3]image]
![[3]](https://2.bp.blogspot.com/-ZWy2xDxXbzg/W98lAuNSY9I/AAAAAAAAHZ0/DFYluvWtz_cwwAUKfblujnW6mTC5XVs1QCLcBGAs/s1600/sphere.png){kind=link}
Maple
plots[display](plottools[sphere](), axes = none, style = surface);Mathematica / Wolfram Language
Mathematica has many 3D drawing capabilities. To create a sphere with radius one centered at (0,0,0):
Graphics3D[Sphere[{0,0,0},1]]
MATLAB
To create the unit sphere:
figure; sphere
Maxima
/* Two solutions */
plot3d(1, [theta, 0, %pi], [phi, 0, 2 * %pi],
[transform_xy, spherical_to_xyz], [grid, 30, 60],
[box, false], [legend, false])$
load(draw)$
draw3d(xu_grid=30, yv_grid=60, surface_hide=true,
parametric_surface(cos(phi)*sin(theta),
sin(phi)*sin(theta),
cos(theta),
theta, 0, %pi, phi, 0, 2 * %pi))$
Nim
import math
type Point = tuple[x,y,z: float]
const shades = ".:!*oe&#%@"
proc normalize(x, y, z: float): Point =
let len = sqrt(x*x + y*y + z*z)
(x / len, y / len, z / len)
proc dot(a, b: Point): float =
result = max(0, - a.x*b.x - a.y*b.y - a.z*b.z)
let light = normalize(30.0, 30.0, -50.0)
proc drawSphere(r: int; k, ambient: float) =
for i in -r .. r:
let x = i.float + 0.5
for j in -2*r .. 2*r:
let y = j.float / 2.0 + 0.5
if x*x + y*y <= float r*r:
let
v = normalize(x, y, sqrt(float(r*r) - x*x - y*y))
b = pow(dot(light, v), k) + ambient
i = clamp(int((1.0 - b) * shades.high.float), 0, shades.high)
stdout.write shades[i]
else: stdout.write ' '
stdout.write "\n"
drawSphere 20, 4.0, 0.1
drawSphere 10, 2.0, 0.4
- Output:
&&&&&&&&&&#######
&eeeeeeeeeeeeeeee&&&&&&#######%
&eoooo*******oooooooeeeee&&&&&########%
eoo****!!!!!!!!******oooooeeee&&&&&########%%
eoo**!!!!::::::::!!!!!*****ooooeeee&&&&&########%%%
eo**!!::::::...:::::::!!!!!***ooooeeee&&&&&########%%%%
eo*!!:::.............:::::!!!!***ooooeeee&&&&&########%%%%%
eo*!!:::.................::::!!!!***ooooeeee&&&&#########%%%%%%
eo*!!::....................::::!!!****oooeeee&&&&&#########%%%%%%
&o**!::......................::::!!!****oooeeee&&&&&##########%%%%%%%
&o**!::.......................::::!!!****oooeeee&&&&&##########%%%%%%%%
&oo*!!::.......................:::!!!!***ooooeeee&&&&&##########%%%%%%%%%
&eo*!!::.......................::::!!!****ooooeeee&&&&&##########%%%%%%%%%%
eo**!!::......................::::!!!!***ooooeeeee&&&&&##########%%%%%%%%%%
&eo**!!:::...................:::::!!!!****ooooeeee&&&&&###########%%%%%%%%%%%
eeo**!!::::................:::::!!!!!****ooooeeee&&&&&&###########%%%%%%%%%%%
&eeo***!!:::::...........::::::!!!!!****oooooeeee&&&&&&###########%%%%%%%%%%%%%
&eeoo**!!!!::::::::::::::::::!!!!!*****ooooeeeee&&&&&&############%%%%%%%%%%%%%
&eeooo***!!!!::::::::::::!!!!!!!*****oooooeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeooo***!!!!!!!!!!!!!!!!!!!******oooooeeeeee&&&&&&############%%%%%%%%%%%%%%%
&&eeeooo******!!!!!!!!!!********ooooooeeeeee&&&&&&&############%%%%%%%%%%%%%%%%
#&&eeeooooo******************oooooooeeeeee&&&&&&&#############%%%%%%%%%%%%%%%%%
#&&&eeeeoooooooo******oooooooooooeeeeeee&&&&&&&&#############%%%%%%%%%%%%%%%%%%
##&&&&eeeeeooooooooooooooooooeeeeeeee&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%
##&&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&################%%%%%%%%%%%%%%%%%%%
####&&&&&&eeeeeeeeeeeeeeeeeee&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%%
#####&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#################%%%%%%%%%%%%%%%%%%%%%%
%#######&&&&&&&&&&&&&&&&&&&&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%
%###########&&&&&&&&&&&&&#######################%%%%%%%%%%%%%%%%%%%%%%%%%
%############################################%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%#########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%#############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::...:::!!!*o
..............::!!*oo
..................::!!**ooe
.....................::!!**ooee
.......................::!!**ooee
........................::!!**oooee
.........................::!!**oooeee
:........................::!!!**oooeeee
........................::!!!**ooooeeee
:......................::!!!***oooeeeee
:....................:::!!!***oooeeeeee
!:.................:::!!!****oooeeeeeee
*!:::...........::::!!!!***ooooeeeeeeee
*!!!:::::::::::!!!!!****oooooeeeeeeee
o**!!!!!!!!!!!!!*****oooooeeeeeeeee
oo**************ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
Ol
(import (lib gl))
(import (OpenGL version-1-0))
; init
(glClearColor 0.3 0.3 0.3 1)
(glPolygonMode GL_FRONT_AND_BACK GL_FILL)
(define quadric (gluNewQuadric))
; draw loop
(gl:set-renderer (lambda (mouse)
(glClear GL_COLOR_BUFFER_BIT)
(glColor3f 0.7 0.7 0.7)
(gluSphere quadric 0.4 32 10)
))
Openscad
Drawing a sphere is easy in openscad:
// This will produce a sphere of radius 5
sphere(5);
OxygenBasic
Using an OpenGl-based console
% Title "Sphere"
'% Animated
% PlaceCentral
uses ConsoleG
sub main
========
cls 0.0, 0.2, 0.7
shading
scale 10
pushstate
GoldMaterial.act
go sphere
popstate
end sub
EndScript
Pascal
After changing "{$APPTYPE CONSOLE}" to "{$mode delphi}" or "{$mode objfpc}" the Delphi example works with FreePascal.
Perl
This produces a PGM image which can't be uploaded on rosettacode at the moment. It looks similar as the Raku solution, though.
use strict;
use warnings;
my $x = my $y = 255;
$x |= 1; # must be odd
my $depth = 255;
my $light = Vector->new(rand, rand, rand)->normalized;
print "P2\n$x $y\n$depth\n";
my ($r, $ambient) = (($x - 1)/2, 0);
my ($r2) = $r ** 2;
{
for my $x (-$r .. $r) {
my $x2 = $x**2;
for my $y (-$r .. $r) {
my $y2 = $y**2;
my $pixel = 0;
if ($x2 + $y2 < $r2) {
my $v = Vector->new($x, $y, sqrt($r2 - $x2 - $y2))->normalized;
my $I = $light . $v + $ambient;
$I = $I < 0 ? 0 : $I > 1 ? 1 : $I;
$pixel = int($I * $depth);
}
print $pixel;
print $y == $r ? "\n" : " ";
}
}
}
package Vector {
sub new {
my $class = shift;
bless ref($_[0]) eq 'Array' ? $_[0] : [ @_ ], $class;
}
sub normalized {
my $this = shift;
my $norm = sqrt($this . $this);
ref($this)->new( map $_/$norm, @$this );
}
use overload q{.} => sub {
my ($a, $b) = @_;
my $sum = 0;
for (0 .. @$a - 1) {
$sum += $a->[$_] * $b->[$_]
}
return $sum;
},
q{""} => sub { sprintf "Vector:[%s]", join ' ', @{shift()} };
}
Phix
(Go gets credit for the dot/normalize/drawSphere routines, but this draws on screen rather than to png file)
Sphere will resize to match the window. You can run this online here. Note fullscreen redraw can be quite slow.
-- -- demo\rosetta\Draw_a_sphere.exw -- ============================== -- with javascript_semantics include pGUI.e constant title = "Draw a sphere" Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas function dot(sequence x, y) return sum(sq_mul(x,y)) end function function normalize(sequence v) atom len = sqrt(dot(v, v)) return iff(len=0?{0,0,0}:sq_mul(v,1/len)) end function procedure drawSphere(integer width, height, atom k, amb, sequence direction) atom t0 = time()+1, t1 = t0, lmul = 255/(1+amb) integer r = floor((min(width,height)-20)/2), cx = floor(width/2), cy = floor(height/2) for x=-r to r do if time()>t1 then -- Let the user know we aren't completely dead just yet IupSetStrAttribute(dlg,"TITLE","%s - drawing (%d%%)",{title,100*(x+r)/(2*r)}) t1 = time()+1 -- (as per DeathStar.exw, prevent "(Not Responding)" nonsense) if platform()!=JS then if IupLoopStep()=IUP_CLOSE then IupExitLoop() exit end if end if end if for y=-r to r do integer z = r*r-(x*x+y*y) if z>=0 then atom s = dot(direction, normalize({x,y,sqrt(z)})), l = iff(s<=0?0:power(s,k)) integer lum = and_bits(#FF,lmul*(l+amb)) cdCanvasPixel(cddbuffer, x+cx, y+cy, lum*#10101) end if end for end for if t1!=t0 then IupSetStrAttribute(dlg,"TITLE",title) end if end procedure function redraw_cb(Ihandle /*ih*/, integer /*posx*/, /*posy*/) integer {width, height} = IupGetIntInt(canvas, "DRAWSIZE") cdCanvasActivate(cddbuffer) cdCanvasClear(cddbuffer) drawSphere(width,height,1.5,0.2,normalize({-30,-30,50})) cdCanvasFlush(cddbuffer) return IUP_DEFAULT end function function map_cb(Ihandle ih) cdcanvas = cdCreateCanvas(CD_IUP, ih) cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas) cdCanvasSetBackground(cddbuffer, CD_BLACK) return IUP_DEFAULT end function procedure main() IupOpen() canvas = IupCanvas("RASTERSIZE=340x340") IupSetCallbacks(canvas, {"MAP_CB", Icallback("map_cb"), "ACTION", Icallback("redraw_cb")}) dlg = IupDialog(canvas,`TITLE="%s"`,{title}) IupShow(dlg) IupSetAttribute(canvas, "RASTERSIZE", NULL) -- release the minimum limitation if platform()!=JS then IupMainLoop() IupClose() end if end procedure main()
PicoLisp
This is for the 64-bit version.
(load "@lib/openGl.l")
(glutInit)
(glutInitDisplayMode (| GLUT_RGBA GLUT_DOUBLE GLUT_ALPHA GLUT_DEPTH))
(glutInitWindowSize 400 400)
(glutCreateWindow "Sphere")
(glEnable GL_LIGHTING)
(glEnable GL_LIGHT0)
(glLightiv GL_LIGHT0 GL_POSITION (10 10 -10 0))
(glEnable GL_COLOR_MATERIAL)
(glColorMaterial GL_FRONT_AND_BACK GL_AMBIENT_AND_DIFFUSE)
(glClearColor 0.3 0.3 0.5 0)
(glColor4f 0.0 0.8 0.0 1.0)
(displayPrg
(glClear (| GL_COLOR_BUFFER_BIT GL_DEPTH_BUFFER_BIT))
(glutSolidSphere 0.9 40 32)
(glFlush)
(glutSwapBuffers) )
# Exit upon mouse click
(mouseFunc '((Btn State X Y) (bye)))
(glutMainLoop)(scl 24)
(setq *Shades
(list "." ":" "!" "*" "o" "e" "&" "#" "%" "@"))
(setq *Light
(list 30.0 30.0 -50.0))
(de normalize (V)
(let Len
(sqrt
(sum
(quote (X)
(** X 2))
V))
(mapcar
(quote (X)
(*/ X 1.0 Len))
V)))
(de dot (X Y)
(let D (sum (quote (A B) (*/ A B 1.0)) X Y)
(if (< D 0) (- D) 0)))
(de floor (N)
(* 1.0 (*/ (- N 0.5) 1.0)))
(de ceil (N)
(* 1.0 (*/ (+ N 0.5) 1.0)))
(de drawSphere (R K Ambient)
(let Vec NIL
(for (I (floor (- R)) (<= I (ceil R)) (+ I 1.0))
(let X (+ I 0.5)
(for (J (floor (* -2 R)) (<= J (ceil (* 2 R))) (+ J 1.0))
(let Y (+ (/ J 2) 0.5)
(if (<= (+ (*/ X X 1.0) (*/ Y Y 1.0)) (*/ R R 1.0))
(prog
(setq Vec
(list X Y
(sqrt
(* 1.0
(- (*/ R R 1.0)
(*/ X X 1.0)
(*/ Y Y 1.0))))))
(setq Vec (normalize Vec))
(let (B NIL
Intensity NIL)
(setq B (+ (/ (** (dot *Light Vec) K) (** 1.0 (- K 1))) Ambient))
(setq Intensity
(if (<= B 0)
(- (length *Shades) 2)
(max (format (round (*/ (- 1.0 B) (* (- (length *Shades) 1) 1.0) 1.0) 0)) 0)))
(prin (nth *Shades (+ Intensity 1) 1))))
(prin " "))))
(prinl)))))
(setq *Light (normalize *Light))
(drawSphere 20.0 4 0.1)
(drawSphere 10.0 2 0.4)- Output:
##############%%%
#&&eeeeeeeeeee&&&&&&######%%%%%
&eeeoooooooooooooeeeee&&&&&######%%%%%%
&eooo**************oooooeeee&&&&&#####%%%%%%%
&eoo**!!!!!!!!!!!!!!*****ooooeeee&&&&######%%%%%%%%
eoo**!!!::::::::::::!!!!****ooooeeee&&&&######%%%%%%%%%
eoo*!!!::::.......::::::!!!!****oooeeee&&&&######%%%%%%%%%%
&eo*!!:::..............::::!!!!***ooooeeee&&&&######%%%%%%%%%%%
eo**!!::.................::::!!!****oooeeee&&&&######%%%%%%%%%%%%
&eo*!!:::..................::::!!!!***oooeeee&&&&&######%%%%%%%%%%%%%
&eo*!!:::...................::::!!!!***oooeeee&&&&&######%%%%%%%%%%%%%%
&eo**!!::....................::::!!!****oooeeee&&&&&######%%%%%%%%%%%%%%%
#eoo*!!:::...................::::!!!!***ooooeeee&&&&#######%%%%%%%%%%%%%%%%
&eo**!!:::.................:::::!!!!****oooeeee&&&&&#######%%%%%%%%%%%%%%%%
&eoo**!!::::...............:::::!!!!****ooooeeee&&&&#######%%%%%%%%%%%%%%%%%%
&eoo**!!!::::...........::::::!!!!*****ooooeeee&&&&&#######%%%%%%%%%%%%%%%%%%
#&eoo***!!!::::::::::::::::::!!!!!****ooooeeeee&&&&&#######%%%%%%%%%%%%%%%%%%%%
#&eeoo***!!!!::::::::::::!!!!!!!*****ooooeeeee&&&&&#######%%%%%%%%%%%%%%%%%%%%%
#&eeooo****!!!!!!!!!!!!!!!!!!******ooooeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%
#&&eeooo******!!!!!!!!!!!*******ooooooeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%%
#&&&eeooooo******************ooooooeeeeee&&&&&&########%%%%%%%%%%%%%%%%%%%%%%%%
##&&&eeeooooooo********oooooooooeeeeeee&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%
###&&&eeeeeooooooooooooooooooeeeeeee&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%%
%###&&&&eeeeeeeeeeeoeeeeeeeeeeeee&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%####&&&&&eeeeeeeeeeeeeeeeee&&&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#####&&&&&&&&&&&&&&&&&&&&&&&&&&&############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######&&&&&&&&&&&&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%############&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%##############################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%#######################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
!::::::!!!**o
............:::!!**oe
:................::!!**ooee
:...................::!!**ooeee
......................::!!**ooeee
.......................::!!**ooeeee
.......................:::!!**ooeeeee
:.......................::!!***ooeeeeee
:......................::!!!**oooeeeeee
:....................:::!!!**oooeeeeeee
!:..................:::!!***oooeeeeeeee
!!:..............::::!!!***oooeeeeeeeee
*!!::::.....::::::!!!!***ooooeeeeeeeeee
o*!!!!::::::!!!!!!****ooooeeeeeeeeeee
o****!!!!!!!******oooooeeeeeeeeeeee
eooo********oooooooeeeeeeeeeeeeee
eeeoooooooooooeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
PostScript
Gradient filled circle:
%!PS-Adobe-3.0
%%BoundingBox 0 0 300 300
150 150 translate 0 0 130 0 360 arc
/Pattern setcolorspace
<< /PatternType 2
/Shading <<
/ShadingType 3
/ColorSpace /DeviceRGB
/Coords [-60 60 0 0 0 100]
/Function <<
/FunctionType 2
/Domain [0 1]
/C0 [1 1 1]
/C1 [0 0 0]
/N 2
>>
>>
>> matrix makepattern setcolor fill
showpage
%%EOF
POV-Ray
This is what POVray was made for. An example with a sky, surface and transparency:
camera { location <0.0 , .8 ,-3.0> look_at 0}
light_source{< 3,3,-3> color rgb 1}
sky_sphere { pigment{ gradient <0,1,0> color_map {[0 color rgb <.2,.1,0>][.5 color rgb 1]} scale 2}}
plane {y,-2 pigment { hexagon color rgb .7 color rgb .5 color rgb .6 }}
sphere { 0,1
texture {
pigment{ color rgbft <.8,1,1,.4,.4> }
finish { phong 1 reflection {0.40 metallic 0.5} }
}
interior { ior 1.5}
}
Yields this:
Processing
3D rendering is built into Processing.
void setup() {
size(500, 500, P3D);
}
void draw() {
background(192);
translate(width/2, height/2);
// optional color and lighting style
stroke(200);
fill(255);
lights();
// draw sphere
sphere(200);
}
A sphere build from triangles (to for instance allow distortion)
float rotX, rotY;
PVector[][] sphere;
int detail = 50;
void setup() {
size(600, 600, P3D);
background(50, 50, 200);
fill(255, 0, 200);
stroke(0, 40);
sphere = new PVector[detail+1][detail+1];
}
void draw() {
pointLight(255, 255, 255, -width, -height, 2*height);
translate(width/2, height/2);
rotateX(rotX);
rotateY(rotY);
float r = 200;
for (int i = 0; i <= detail; i++) {
float rows = map(i, 0, detail, 0, PI);
for (int j = 0; j <= detail; j++) {
float columns = map(j, 0, detail, 0, TWO_PI);
float x = r * sin(rows) * cos(columns);
float y = r * sin(rows) * sin(columns);
float z = r * cos(rows);
sphere[i][j] = new PVector(x, y, z);
}
}
for (int i = 0; i < detail; i++) {
beginShape(TRIANGLE_STRIP);
for (int j = 0; j <= detail; j++) {
PVector v1 = sphere[i][j];
vertex(v1.x, v1.y, v1.z);
PVector v2 = sphere[i+1][j];
vertex(v2.x, v2.y, v2.z);
}
endShape();
}
}
void mouseDragged() {
rotY -= (mouseX - pmouseX) * 0.01;
rotX -= (mouseY - pmouseY) * 0.01;
}
Python
Ascii-Art
import math
shades = ('.',':','!','*','o','e','&','#','%','@')
def normalize(v):
len = math.sqrt(v[0]**2 + v[1]**2 + v[2]**2)
return (v[0]/len, v[1]/len, v[2]/len)
def dot(x,y):
d = x[0]*y[0] + x[1]*y[1] + x[2]*y[2]
return -d if d < 0 else 0
def draw_sphere(r, k, ambient, light):
for i in range(int(math.floor(-r)),int(math.ceil(r)+1)):
x = i + 0.5
line = ''
for j in range(int(math.floor(-2*r)),int(math.ceil(2*r)+1)):
y = j/2 + 0.5
if x*x + y*y <= r*r:
vec = normalize((x,y,math.sqrt(r*r - x*x - y*y)))
b = dot(light,vec)**k + ambient
intensity = int((1-b)*(len(shades)-1))
line += shades[intensity] if 0 <= intensity < len(shades) else shades[0]
else:
line += ' '
print(line)
light = normalize((30,30,-50))
draw_sphere(20,4,0.1, light)
draw_sphere(10,2,0.4, light)
- Output:
&&&&&&&&&&######
&&eeeeeeeeeeeeeeee&&&&&&######%%
&&oooo********ooooooeeeeee&&&&########%%
oo****!!!!!!!!******ooooooeeee&&&&########%%
eeoo**!!!!::::::::!!!!******ooooeeee&&&&########%%%%
ee**!!::::::....::::::!!!!!!**ooooeeee&&&&&&########%%%%
ee**!!::..............::::!!!!****ooooeeee&&&&########%%%%%%
ee**!!::..................::::!!!!**ooooeeee&&&&##########%%%%%%
oo!!::....................::::!!!!****ooeeee&&&&&&########%%%%%%
oo**::......................::::!!!!****ooeeee&&&&&&##########%%%%%%
&&**!!::......................::::!!!!****ooeeee&&&&&&##########%%%%%%%%
oo**!!::......................::::!!!!**ooooeeee&&&&&&##########%%%%%%%%
&&oo!!::........................::::!!****ooooeeee&&&&&&##########%%%%%%%%%%
ee**!!::......................::::!!!!****ooooeeee&&&&&&##########%%%%%%%%%%
ee**!!::::..................::::::!!!!****ooooeeee&&&&############%%%%%%%%%%
ee**!!::::................::::::!!!!****ooooeeee&&&&&&############%%%%%%%%%%
&&ee****!!::::............::::::!!!!****ooooooeeee&&&&&&##########%%%%%%%%%%%%%%
&&eeoo**!!!!::::::::::::::::::!!!!******ooooeeee&&&&&&############%%%%%%%%%%%%%%
&&eeoo****!!!!::::::::::::!!!!!!******ooooeeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeoooo**!!!!!!!!!!!!!!!!!!!!******ooooeeeeee&&&&&&############%%%%%%%%%%%%%%%%
&&eeeeoo******!!!!!!!!!!********ooooooeeeeee&&&&&&&&############%%%%%%%%%%%%%%%%
##&&eeoooooo******************ooooooeeeeee&&&&&&&&############%%%%%%%%%%%%%%%%%%
##&&eeeeoooooooo******ooooooooooooeeeeee&&&&&&&&##############%%%%%%%%%%%%%%%%%%
##&&&&eeeeeeooooooooooooooooooeeeeeeee&&&&&&&&##############%%%%%%%%%%%%%%%%%%%%
##&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&&################%%%%%%%%%%%%%%%%%%
####&&&&&&eeeeeeeeeeeeeeeeee&&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%
######&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&##################%%%%%%%%%%%%%%%%%%%%%%
%%######&&&&&&&&&&&&&&&&&&&&&&&&####################%%%%%%%%%%%%%%%%%%%%%%%%
############&&&&&&&&&&&&########################%%%%%%%%%%%%%%%%%%%%%%%%
%%############################################%%%%%%%%%%%%%%%%%%%%%%%%%%
%%######################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%##############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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::..::::!!**
..............::!!oo
..................::!!**ooee
......................::!!**ooee
......................::!!**ooee
........................::!!**ooooee
........................::!!**ooooee
::........................::!!**ooooeeee
........................::!!!!**ooooeeee
::......................::!!****ooeeeeee
::....................::!!!!**ooooeeeeee
!!..................::!!!!****ooeeeeeeee
**::::..........::::!!!!****ooooeeeeeeee
!!!!::::::::::!!!!!!****ooooeeeeeeee
oo**!!!!!!!!!!!!******ooooeeeeeeeeee
oo**************ooooooeeeeeeeeee
eeooooooooooooooooeeeeeeeeeeeeee
eeeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeee
eeeeeeeeeeee
Renders a sphere with random Perlin noise.
This code contains unnecessary functions which are part of a 3D graphics library I wrote.
Uses Pygame and Python 3.2.2
import pygame
from pygame.locals import *
import time
import sys
import random
import math
class Tricubic:
def __init__(self,pts):
self.coefficients = []
for plane in pts:
planecoeffs = []
for line in plane:
p = (line[3]-line[2])-(line[0]-line[1])
q = (line[0]-line[1])-p
r = line[2]-line[0]
s = line[1]
planecoeffs.append([p,q,r,s])
self.coefficients.append(planecoeff)
def Eval(at):
return Misc.Cubic([CoeffBicubic(coeffs[0],d),CoeffBicubic(coeffs[1],d),CoeffBicubic(coeffs[2],d),CoeffBicubic(coeffs[3],d)],d.z)
def CoeffCubic(coeffs,d):
return (coeffs[0]*(d.x**3))+(coeffs[1]*(d.x**2))+(coeffs[2]*d.x)+coeffs[3]
def CoeffBicubic(coeffs,d):
return Misc.Cubic([CoeffCubic(coeffs[0],d),CoeffCubic(coeffs[1],d),CoeffCubic(coeffs[2],d),CoeffCubic(coeffs[3],d)],d.y)
class Misc:
def LinePara(line,t):
return Vector3.Add(line[0],Vector3.Scale(Vector3.Subtract(line[1],line[0]),t))
def LUR(at,above):
look = at.Unit()
right = Vector3.Cross(look,above).Unit()
up = Vector3.Scale(Vector3.Cross(look,right),-1)
return [look,up,right]
def LinePlane(line,triangle,cp=True):
try:
u = Vector3.Subtract(triangle.points[1].point,triangle.points[0])
v = Vector3.Subtract(triangle.points[2],triangle.points[0])
n = Vector3.Cross(u,v)
r = (Vector3.Dot(n,Vector3.Subtract(triangle.points[0],line.start))/Vector3.Dot(n,line.direction))
if stp:
point = Vector3.Add(Vector3.Scale(line.direction,r),line.start)
w = Vector3.Subtract(point,triangle.points[0])
udv = Vector3.Dot(u,v)
wdv = Vector3.Dot(w,v)
vdv = Vector3.Dot(v,v)
wdu = Vector3.Dot(w,u)
udu = Vector3.Dot(u,u)
denominator = (udv**2)-(udu*vdv)
s = ((udv*wdv)-(vdv*wdu))/denominator
t = ((udv*wdu)-(udu*wdv))/denominator
return [r,Vector2(s,t),point]
print('hooray')
else:
return [r]
except:
return None
def Cubic(pts,d):
p = (pts[3]-pts[2])-(pts[0]-pts[1])
q = (pts[0]-pts[1])-p
r = pts[2]-pts[0]
s = pts[1]
return (p*(d**3))+(q*(d**2))+(r*d)+s
def Bicubic(pts,d):
return Misc.Cubic([Misc.Cubic(pts[0],d.x),Misc.Cubic(pts[1],d.x),Misc.Cubic(pts[2],d.x),Misc.Cubic(pts[3],d.x)],d.y)
def Tricubic(pts,d):
return Misc.Cubic([Misc.Bicubic(pts[0],d),Misc.Bicubic(pts[1],d),Misc.Bicubic(pts[2],d),Misc.Bicubic(pts[3],d)],d.z)
def Quadcubic(pts,d):
return Misc.Cubic([Misc.Tricubic(pts[0],d),Misc.Tricubic(pts[1],d),Misc.Tricubic(pts[2],d),Misc.Tricubic(pts[3],d)],d.w)
def Linear(pts,d):
return (pts[2]*d)+(pts[1]*(1-d))
def Bilinear(pts,d):
return Misc.Linear([0,Misc.Linear(pts[1],d.x),Misc.Linear(pts[2],d.x)],d.y)
def Trilinear(pts,d):
return Misc.Linear([0,Misc.Bilinear(pts[1],d),Misc.Bilinear(pts[2],d)],d.z)
def LP2(line,triangle,cp=True):
try:
bla = triangle.points[1]
bla = triangle.points[0]
u = Vector3.Subtract(triangle.points[1].point,triangle.points[0].point)
v = Vector3.Subtract(triangle.points[2].point,triangle.points[0].point)
n = Vector3.Cross(u,v)
d = Vector3.Subtract(line[1],line[0])
r = (Vector3.Dot(n,Vector3.Subtract(triangle.points[0].point,line[0]))/Vector3.Dot(n,d))
if cp:
point = Vector3.Add(Vector3.Scale(d,r),line[0])
w = Vector3.Subtract(point,triangle.points[0].point)
udv = Vector3.Dot(u,v)
wdv = Vector3.Dot(w,v)
vdv = Vector3.Dot(v,v)
wdu = Vector3.Dot(w,u)
udu = Vector3.Dot(u,u)
denominator = (udv**2)-(udu*vdv)
s = ((udv*wdv)-(vdv*wdu))/denominator
t = ((udv*wdu)-(udu*wdv))/denominator
return (r,Vector2(s,t),point)
else:
return (r)
except:
return None
def Phong(normal,viewer,light,material,term):
# light (vector_to,diffuse,specular)
# material (ambient,diffuse,specular,shininess)
n = normal.Unit()
v = viewer.Unit()
l = light[0].Unit()
ldn = Vector3.Dot(l,n)
#print(ldn)
val = 0
if ldn > 0:
val += material[1][term]*ldn*light[1][term]
rdv = Vector3.Dot(Vector3.Subtract(Vector3.Scale(n,2*ldn),l),v)
if rdv > 0:
val += (material[2][term]*(rdv**material[3])*light[2][term])
#print(val)
return val
def Lighting(ambient,normal,viewer,lights,material,term):
# lights [(vector_to,diffuse,specular)]
# material (ambient,diffuse,specular,shininess)
val = material[0][term]*ambient[term]
for light in lights:
val += Misc.Phong(normal,viewer,light,material,term)
return val
def Lighting2(start,direction,ambient,intersect,triangle,lights):
coord = intersect[1]
val = Color.Add(Color.Multiply(ambient,Color.Multiply(triangle.material.color['ambient'],triangle.Map('ambient',coord))),
Color.Multiply(triangle.material.color['glow'],triangle.Map('glow',coord)))
for light in lights:
for n in range(3):
val[n] += Misc.Phong(triangle.InterpolatedNormal(coord),
Vector3.Scale(direction,-1),
(light.To(intersect[2]),light.Diffuse(intersect[2]),light.Specular(intersect[2])),
(Color(),
Color.Multiply(triangle.material.color['diffuse'],triangle.Map('diffuse',coord)),
Color.Multiply(triangle.material.color['specular'],triangle.Map('specular',coord)),
triangle.material.shiny),n)
return val
def Ray(start,direction,scene,color=True,sector=None):
intersect = None
intersected = None
col = None
for triangle in scene.triangles:
possible = True
if sector != None:
possible = False
for point in triangle.points:
if not(point.sector.x < sector.x):
possible = True
if possible:
possible = False
for point in triangle.points:
if not(point.sector.x > sector.x):
possible = True
if possible:
possible = False
for point in triangle.points:
if not(point.sector.y < sector.y):
possible = True
if possible:
possible = False
for point in triangle.points:
if not(point.sector.y > sector.y):
possible = True
possible = True
if possible:
tmp = Misc.LP2([start,Vector3.Add(start,direction)],triangle,color)
write = False
if type(tmp) == type(5.1):
tmp = None
if (tmp != None):
if (intersect == None):
if (tmp[0] > 0) and (tmp[1].x >= 0) and (tmp[1].y >= 0) and (tmp[1].x+tmp[1].y <= 1):
write = True
elif (tmp[0] > 0) and (tmp[0] < intersect[0]) and (tmp[1].x >= 0) and (tmp[1].y >= 0) and (tmp[1].x+tmp[1].y <= 1):
write = True
if write:
intersect = tmp
intersected = triangle
if color and (intersect != None):
applicable = []
for light in scene.lights:
block = Misc.Ray(intersect[2],light.To(intersect[2]),scene,False)
if block == None:
applicable.append(light)
elif light.location != None:
if Vector3.Subtract(light.location,intersect[2]).Magnitude() < block[0]:
applicable.append(light)
col = Misc.Lighting2(start,direction,scene.ambient,intersect,intersected,applicable)
return (intersect,col)
else:
return intersect
class DirLight:
def __init__(self,direction,diffuse,specular):
self.location = None
self.direction = direction.Unit()
self.diffuse = diffuse
self.specular = specular
def To(self,frm):
return Vector3.Scale(self.direction,-1)
def Diffuse(self,to):
return self.diffuse
def Specular(self,to):
return self.specular
class Material:
def __init__(self):
self.color = {'ambient':Color(1,1,1),
'diffuse':Color(1,1,1),
'specular':Color(1,1,1),
'glow':Color(1,1,1)}
self.maps = {'ambient':Map(),
'diffuse':Map(),
'specular':Map(),
'glow':Map(),
'bump':Map()}
self.shiny = 10
class Map:
def __init__(self,surface=None):
self.surface = surface
if self.surface != None:
self.width = self.surface.get_width()
self.height = self.surface.get_height()
def __getitem__(self,index):
if self.surface == None:
return Color(1,1,1)
else:
try:
return Color.From255(self.surface.get_at((int(index.x*(self.width-1)),int(index.y*(self.height-1)))))
except:
return Color(0,0,1)
class Color:
def __init__(self,r=0,g=0,b=0):
self.r = r
self.g = g
self.b = b
def __getitem__(self,index):
if index == 0:
return self.r
elif index == 1:
return self.g
elif index == 2:
return self.b
def __setitem__(self,index,value):
if index == 0:
self.r = value
elif index == 1:
self.g = value
elif index == 2:
self.b = value
def Multiply(A,B):
return Color(A.r*B.r,A.g*B.g,A.b*B.b)
def Add(A,B):
return Color(A.r+B.r,A.g+B.g,A.b+B.b)
def From255(A):
return Color(A.r/255,A.g/255,A.b/255)
class Vertex:
def __init__(self,point,normal,maps):
self.bpoint = point
self.bnormal = normal
self.maps = maps
for name in ['ambient','diffuse','specular','glow','bump']:
try:
bla = self.maps[name]
except:
self.maps[name] = Vector2()
self.sector = None
def Transform(self,points,norms):
self.point = Matrix2.Multiply(self.bpoint.Horizontal(),points).Vectorize()
self.normal = Matrix2.Multiply(self.bnormal.Horizontal(),norms).Vectorize()
class Triangle:
def __init__(self,vertices,material=Material()):
self.points = vertices
self.material = material
def Map(self,name,coord):
pts = []
for n in range(3):
pts.append(self.points[n].maps[name])
loc = Vector2.Add(pts[0],
Vector2.Add(Vector2.Scale(Vector2.Subtract(pts[1],pts[0]),coord.x),
Vector2.Scale(Vector2.Subtract(pts[2],pts[0]),coord.y)))
#print(loc.x,loc.y)
return self.material.maps[name][loc]
def InterpolatedNormal(self,coord):
return Vector3.Add(Vector3.Scale(self.points[0].normal,1-coord.x-coord.y),
Vector3.Add(Vector3.Scale(self.points[1].normal,coord.x),Vector3.Scale(self.points[2].normal,coord.y))).Unit()
class Line:
def __init__(self,A,B=None,direction=None):
self.start = A
if B != None:
self.direction = Vector3.Subtract(B,A).Unit()
elif direction != None:
self.direction = direction
else:
raise RuntimeError('Neither B nor direction are specified')
class Scene:
def __init__(self):
self.triangles = []
self.vertices = []
self.lights = []
self.exterior = []
self.ambient = 0
class Matrix2:
def __init__(self,data=[[]]):
self.FromData(data)
def __getitem__(self,index):
return self.data[index[1]][index[0]]
def __setitem__(self,index,value):
self.data[index[1]][index[0]]=value
def Dimension(self):
self.rows = len(self.data)
self.cols = len(self.data[0])
def FromData(self,data):
self.data = data
length=len(data[0])
for row in data:
if len(row)!=length:
self.data=None
raise RuntimeError('Data rows are not of uniform length.')
self.Dimension()
def Multiply(A,B):
if A.cols!=B.rows:
raise RuntimeError('Column count of Matrix2 \"A\" does not match row count of Matrix2 \"B\".')
matrix = Matrix2.Empty(B.cols,A.rows)
x=0
while x<matrix.cols:
y=0
while y<matrix.rows:
val=0
n=0
while n<A.cols:
val+=A[(n,y)]*B[(x,n)]
n+=1
matrix[(x,y)]=val
y+=1
x+=1
return matrix
def Scalar(A,n):
pass
def Empty(rows,cols):
data = []
row = [0]*rows
n = 0
while n < cols:
data.append(row[:])
n+=1
matrix=Matrix2(data)
matrix.Dimension()
return matrix
def Identity(cols):
matrix = Matrix2.Empty(cols,cols)
n = 0
while n < cols:
matrix[(n,n)]=1
n += 1
return matrix
def Vectorize(self):
if self.cols==1:
if self.rows!=4:
raise RuntimeError('Only 1 by 4 or 4 by 1 Matrix2s can be cast to Vector3s.')
vertical=True
elif self.rows==1:
if self.cols!=4:
raise RuntimeError('Only 1 by 4 or 4 by 1 Matrix2s can be cast to Vector3s.')
vertical = False
else:
raise RuntimeError('Only 1 by 4 or 4 by 1 Matrix2s can be cast to Vector3s.')
vector=[0]*4
n=0
while n<4:
if vertical:
vector[n]=self[(0,n)]
else:
vector[n]=self[(n,0)]
n+=1
return Vector3(vector[0],vector[1],vector[2],vector[3])
def Print(self,decimals,spaces):
length=0
for row in self.data:
for val in row:
string=str(round(val,decimals))
if length<len(string):
length=len(string)
text=''
for row in self.data:
temp=''
for value in row:
val=str(round(float(value),decimals))
pads=length-len(val)
pad=int(pads/2)
temp+=(' '*pad)+val+(' '*(pads-pad))+(' '*spaces)
text+=(' '*spaces)+temp[0:len(temp)-1]+(' '*spaces)+'\n'
return(text[0:len(text)-1])
def RotX(angle):
return Matrix2([
[1,0,0,0],
[0,math.cos(angle),0-math.sin(angle),0],
[0,math.sin(angle),math.cos(angle),0],
[0,0,0,1]])
def RotY(angle):
return Matrix2([
[math.cos(angle),0,0-math.sin(angle),0],
[0,1,0,0],
[math.sin(angle),0,math.cos(angle),0],
[0,0,0,1]])
def RotZ(angle):
return Matrix2([
[math.cos(angle),0-math.sin(angle),0,0],
[math.sin(angle),math.cos(angle),0,0],
[0,0,1,0],
[0,0,0,1]])
def Translate(vector):
return Matrix2([
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[vector.x,vector.y,vector.z,1]])
def Scale(vector):
return Matrix2([
[vector.x,0,0,0],
[0,vector.y,0,0],
[0,0,vector.z,0],
[0,0,0,1]])
def Clone(self):
data = []
for row in self.data:
data.append(row[:])
return Matrix2(data)
def Inverse(self):
adjoint = self.Adjoint()
det = self.Determinant()
if det == 0:
raise RuntimeError('Cannot find the inverse of a matrix with a determinant of 0')
inverse = Matrix2.Empty(self.rows,self.cols)
x = 0
while x < self.cols:
y = 0
while y < self.rows:
inverse[(x,y)] = adjoint[(x,y)]/det
y += 1
x += 1
return inverse
def Transpose(self):
transpose = Matrix2.Empty(self.cols,self.rows)
x = 0
while x < self.cols:
y = 0
while y < self.rows:
transpose[(y,x)] = self[(x,y)]
y += 1
x += 1
return transpose
def Adjoint(self):
return self.Cofactors().Transpose()
def Determinant(self):
if self.rows != self.cols:
raise RuntimeError('Cannot find the determinant of a non-square matrix')
if self.rows == 1:
return self[(0,0)]
cofactors = self.Cofactors()
determinant = 0
n = 0
while n < self.cols:
determinant += self[(n,0)]*cofactors[(n,0)]
n += 1
return determinant
def Minors(self):
if self.rows != self.cols:
raise RuntimeError('Cannot find the minors of a non-square matrix')
if self.rows == 1:
raise RuntimeError('Cannot find the minors of a 1 by 1 matrix')
minors = Matrix2.Empty(self.rows,self.cols)
lines = range(self.rows)
x = 0
while x < self.cols:
y = 0
while y < self.cols:
tiny = Matrix2.Empty(self.rows-1,self.cols-1)
ox = 0
nx = 0
while ox < self.cols:
oy = 0
ny = 0
while oy < self.cols:
if not((ox == x) or (oy == y)):
tiny[(nx,ny)] = self[(ox,oy)]
if oy != y:
ny += 1
oy += 1
if ox != x:
nx += 1
ox += 1
minors[(x,y)] = tiny.Determinant()
y += 1
x += 1
return minors
def Cofactors(self):
minors = self.Minors()
cofactors = Matrix2.Empty(self.rows,self.cols)
x = 0
while x < self.cols:
y = 0
while y < self.rows:
if int((x+y)/2) == ((x+y)/2):
cofactors[(x,y)] = minors[(x,y)]
else:
cofactors[(x,y)] = -1*minors[(x,y)]
y += 1
x += 1
return cofactors
def Perspective(e):
return Matrix2([
[1,0,0,0],
[0,1,0,0],
[0,0,1,1/e[2]],
[-e[0],-e[1],0,0]])
def Add(A,B):
if A.rows != B.rows:
RuntimeError('The row counts of Matrix \"A\" and Matrix \"B\" are not identical.')
if A.cols != B.cols:
RuntimeError('The column counts of Matrix \"A\" and Matrix \"B\" are not identical.')
matrix = Matrix.Empty(A.rows,A.cols)
for x in range(A.cols):
for y in range(A.rows):
matrix[(x,y)] = A[(x,y)]+B[(x,y)]
return matrix
def Subtract(A,B):
if A.rows != B.rows:
RuntimeError('The row counts of Matrix \"A\" and Matrix \"B\" are not identical.')
if A.cols != B.cols:
RuntimeError('The column counts of Matrix \"A\" and Matrix \"B\" are not identical.')
matrix = Matrix.Empty(A.rows,A.cols)
for x in range(A.cols):
for y in range(A.rows):
matrix[(x,y)] = A[(x,y)]+B[(x,y)]
return matrix
def DivHomogeneous(self):
if (self.cols,self.rows) == (1,4):
for y in range(3):
self[(0,y)] = self[(0,y)]/self[(0,3)]
self[(0,3)] = 1
if (self.cols,self.rows) == (4,1):
for x in range(3):
self[(x,0)] = self[(x,0)]/self[(3,0)]
self[(3,0)] = 1
else:
raise RuntimeError('1 by 4 or 4 by 1 Matrix2 expected')
def Object(pos,look,up,right):
return Matrix2([
[right.x,right.y,right.z,0],
[up.x,up.y,up.z,0],
[look.x,look.y,look.z,0],
[pos.x,pos.y,pos.z,1]])
def Camera(eye,look,up,right):
return Matrix2([
[right.x,up.x,look.x,0],
[right.y,up.y,look.y,0],
[right.z,up.z,look.z,0],
[-Vector3.Dot(eye,right),
-Vector3.Dot(eye,up),
-Vector3.Dot(eye,look),1]])
def YPR(rot):
return Matrix2.Multiply(
Matrix2.Multiply(Matrix2.RotZ(rot.z),
Matrix2.RotX(rot.x)),
Matrix2.RotY(rot.y))
class Vector2:
def __init__(self,data=0,y=0):
if (type(data) == type(5)) or (type(data) == type(5.1)):
self.x = data
self.y = y
else:
self.x = data[0]
self.y = data[1]
def __getitem__(self,index):
if index == 0:
return self.x
elif index == 1:
return self.y
def __setitem__(self,index,value):
if index == 0:
self.x = value
elif index == 1:
self.y = 1
def Add(A,B):
return Vector2(A.x+B.x,A.y+B.y)
def Subtract(A,B):
return Vector2(A.x-B.x,A.y-B.y)
def Scale(A,n):
return Vector2(A.x*n,A.y*n)
def Magnitude(self):
return ((self.x**2)+(self.y**2))**.5
def Unit(self):
return Vector2.Scale(self,1/self.Magnitude())
def Clone(self):
return Vector2(self.x,self.y)
class Vector3:
def __init__(self,data=0,y=0,z=0,w=1):
if (type(data) == type(5)) or (type(data) == type(5.1)):
self.x = data/w
self.y = y/w
self.z = z/w
else:
try:
temp = data[3]
except:
temp = 1
self.x = data[0]/temp
self.y = data[1]/temp
self.z = data[2]/temp
def __getitem__(self,index):
if index == 0:
return self.x
elif index == 1:
return self.y
elif index == 2:
return self.z
def __setitem__(self,index,value):
if index == 0:
self.x = value
elif index == 1:
self.y = value
elif index == 2:
self.z = value
def Vertical(self):
return Matrix2([[self.x],[self.y],[self.z],[1]])
def Horizontal(self):
return Matrix2([[self.x,self.y,self.z,1]])
def Dot(A,B):
return (A.x*B.x)+(A.y*B.y)+(A.z*B.z)
def Cross(A,B):
return Vector3([
(A.y*B.z)-(A.z*B.y),
(A.z*B.x)-(A.x*B.z),
(A.x*B.y)-(A.y*B.x)])
def Add(A,B):
return Vector3(A.x+B.x,A.y+B.y,A.z+B.z)
def Subtract(A,B):
return Vector3(A.x-B.x,A.y-B.y,A.z-B.z)
def Scale(A,n):
return Vector3(A.x*n,A.y*n,A.z*n)
def Magnitude(self):
return ((self.x**2)+(self.y**2)+(self.z**2))**.5
def Print(self,decimals,spaces):
return self.Horizontal().Print(decimals,spaces)
def Same(A,B):
same = False
if A.x == B.x:
if A.y == B.y:
if A.z == B.z:
same = True
return same
def Unit(self):
return Vector3.Scale(self,1/self.Magnitude())
def Clone(self):
return Vector3(self.x,self.y,self.z)
class Vector4:
def __init__(self,data=0,y=0,z=0,w=0):
if (type(data) == type(5)) or (type(data) == type(5.1)):
self.x = data
self.y = y
self.z = z
self.w = w
else:
self.x = data[0]
self.y = data[0]
self.z = data[0]
self.w = data[0]
points = [Vector3([-1,-1,0]),Vector3([1,-1,0]),Vector3([0,1,0])]
width = 255
height = width
screen = pygame.display.set_mode((width,height),0,32)
scl = 2
pos = Vector3([0,0,5])
view = Vector3([0,0,1])
frames = 0
def Transform(point,mat):
return Matrix2.Multiply(point.Horizontal(),mat).Vectorize()
def RV():
return Vector3([random.random(),random.random(),random.random()])
green = pygame.Color(0,255,0)
def XY(bla):
return (((width*bla[0])+width)/2,((height*bla[1])+width)/2)
screen.fill(pygame.Color(0,0,0))
size = 255
world = Matrix2.Identity(4)
inv = world.Inverse()
invt = world.Inverse().Transpose()
center = Vector3(0,0,2)
def Texture(size):
texture = []
for pa in range(size):
plane = []
for pb in range(size):
line = []
for pc in range(size):
line.append(random.random())
plane.append(line)
texture.append(plane)
return texture
lights = [(Vector3(-10,6,-9),[.7,.7*.9,.7*.8],[.7,.7*.9,.9*.8])]
lights = [(Vector3(-10,6,-9),[.8,.8,.8],[.7,.7,.7])]
depth = 3
groups = []
for n in range(1):
textures = []
for n in range(depth):
textures.append(Texture(4**(n+1)))
groups.append(textures)
def Select(texture,at):
sel = []
for pa in range(4):
aplane = texture[pa+math.floor(at.z)]
bplane = []
for pb in range(4):
aline = aplane[pb+math.floor(at.y)]
bline = []
for pc in range(4):
bline.append(aline[pc+math.floor(at.x)])
bplane.append(bline)
sel.append(bplane)
return (sel,Vector3(at.x%1,at.y%1,at.z%1))
def Round(val):
return val-(val-math.floor(val))
theta = math.tan(70*math.pi/360)
for x in range(width):
for event in pygame.event.get():
if event.type == QUIT:
pygame.quit()
sys.exit()
if event.type == KEYDOWN:
pass
for y in range(height):
l = Vector3(theta*2*((x/width)-.5),theta*2*((y/width)-.5),1).Unit()
ldc = Vector3.Dot(l,center)
d = ldc-(((ldc**2)-Vector3.Dot(center,center)+1)**.5)
if type(d) != type((-1)**.5):
intersection = Vector3.Scale(l,d)
normal = Vector3.Subtract(intersection,center).Unit()
point = Transform(normal,world)
s = Vector3.Scale(Vector3.Add(point,Vector3(1,1,1)),.5)
val = 0
for i in range(depth):
sel = Select(groups[0][i],Vector3.Scale(s,4**i))
val += Misc.Tricubic(sel[0],sel[1])*((1/2)**i)/4
val = (25*val)%1
vals = [0,Misc.Linear([0,.3,1],val),1]
coloring = []
for i in range(3):
#light = Misc.Lighting([1,1,1],normal,Vector3.Scale(intersection,-1),lights,([0,.03*val,.03],[0,.7*val,.7],[.3,.3,.3],7),i)
light = Misc.Lighting([.1,.1,.1],normal,Vector3.Scale(intersection,-1),lights,(vals,vals,[1,1,1],10),i)
if light > 1:
light = 1
elif light < 0:
light = 0
coloring.append(round(255*light))
screen.set_at((x,height-y),pygame.Color(coloring[0],coloring[1],coloring[2]))
pygame.display.update()
pygame.image.save(screen,"PythonSphere.png")
while True:
for event in pygame.event.get():
if event.type == QUIT:
pygame.quit()
sys.exit()
if event.type == KEYDOWN:
pass
Short version:
from visual import *
scene.title = "VPython: Draw a sphere"
sphere() # using defaults, see http://www.vpython.org/contents/docs/defaults.html
Regular version, with some window-dressing:
from __future__ import print_function, division
from visual import *
title = "VPython: Draw a sphere"
scene.title = title
print( "%s\n" % title )
print( 'Drag with right mousebutton to rotate view' )
print( 'Drag up+down with middle mousebutton to zoom')
scene.autocenter = True
# uncomment any (or all) of those variants:
S1 = sphere(pos=(0.0, 0.0, 0.0), radius=1.0, color=color.blue)
#S2 = sphere(pos=(2.0, 0.0, 0.0), radius=1.0, material=materials.earth)
#S3 = sphere(pos=(0.0, 2.0, 0.0), radius=1.0, material=materials.BlueMarble)
#S4 = sphere(pos=(0.0, 0.0, 2.0), radius=1.0,
# color=color.orange, material=materials.marble)
while True: # Animation-loop
rate(100)
pass # no animation in this demo
Racket
Using the Typed Racket language with the plot library:
#lang typed/racket
(require plot/typed)
(plot3d (polar3d (λ (θ ρ) 1)) #:altitude 25)
Raku
(formerly Perl 6)
Pure Raku
The C code is modified to output a .pgm file.
my $width = my $height = 255; # must be odd
my @light = normalize([ 3, 2, -5 ]);
my $depth = 255;
sub MAIN ($outfile = 'sphere-perl6.pgm') {
spurt $outfile, "P5\n$width $height\n$depth\n"; # .pgm header
my $out = open( $outfile, :a, :bin ) orelse .die;
$out.write( Blob.new(draw_sphere( ($width-1)/2, .9, .2) ) );
$out.close;
}
sub normalize (@vec) { @vec »/» ([+] @vec »*« @vec).sqrt }
sub dot (@x, @y) { -([+] @x »*« @y) max 0 }
sub draw_sphere ( $rad, $k, $ambient ) {
my @pixels[$height];
my $r2 = $rad * $rad;
my @range = -$rad .. $rad;
@range.hyper.map: -> $x {
my @row[$width];
@range.map: -> $y {
if (my $x2 = $x * $x) + (my $y2 = $y * $y) < $r2 {
my @vector = normalize([$x, $y, ($r2 - $x2 - $y2).sqrt]);
my $intensity = dot(@light, @vector) ** $k + $ambient;
my $pixel = (0 max ($intensity * $depth).Int) min $depth;
@row[$y+$rad] = $pixel;
}
else {
@row[$y+$rad] = 0;
}
}
@pixels[$x+$rad] = @row;
}
flat |@pixels.map: *.list;
}
Cairo graphics library
use Cairo;
given Cairo::Image.create(Cairo::FORMAT_ARGB32, 256, 256) {
given Cairo::Context.new($_) {
my Cairo::Pattern::Solid $bg .= create(.5,.5,.5);
.rectangle(0, 0, 256, 256);
.pattern($bg);
.fill;
$bg.destroy;
my Cairo::Pattern::Gradient::Radial $shadow .=
create(105.2, 102.4, 15.6, 102.4, 102.4, 128.0);
$shadow.add_color_stop_rgba(0, .3, .3, .3, .3);
$shadow.add_color_stop_rgba(1, .1, .1, .1, .02);
.pattern($shadow);
.arc(136.0, 134.0, 110, 0, 2 * pi);
.fill;
$shadow.destroy;
my Cairo::Pattern::Gradient::Radial $sphere .=
create(115.2, 102.4, 25.6, 102.4, 102.4, 128.0);
$sphere.add_color_stop_rgba(0, 1, 1, .698, 1);
$sphere.add_color_stop_rgba(1, .923, .669, .144, 1);
.pattern($sphere);
.arc(128.0, 128.0, 110, 0, 2 * pi);
.fill;
$sphere.destroy;
};
.write_png('sphere2-perl6.png');
}
See sphere2-perl6.png (offsite .png image)
REXX
This program is modeled after the C version.
The REXX language doesn't have a SQRT function, so a version is included here.
Same with the CEILing and FLOOR functions.
Programming note: the output will appear slightly different when executed on an EBCDIC machine (due to different dithering characters).
/*REXX program expresses a lighted sphere with simple characters used for shading. */
call drawSphere 19, 4, 2/10, '30 30 -50' /*draw a sphere with a radius of 19. */
call drawSphere 10, 2, 4/10, '30 30 -50' /* " " " " " " " ten. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
ceil: procedure; parse arg x; _= trunc(x); return _ +(x>0) * (x\=_)
floor: procedure; parse arg x; _= trunc(x); return _ -(x<0) * (x\=_)
norm: parse arg $a $b $c; _= sqrt($a**2 + $b**2 + $c**2); return $a/_ $b/_ $c/_
/*──────────────────────────────────────────────────────────────────────────────────────*/
drawSphere: procedure; parse arg r, k, ambient, lightSource /*obtain the four arguments*/
if 8=='f8'x then shading= ".:!*oe&#%@" /* EBCDIC dithering chars. */
else shading= "·:!°oe@░▒▓" /* ASCII " " */
parse value norm(lightSource) with s1 s2 s3 /*normalize light source. */
shadeLen= length(shading) - 1; rr= r**2; r2= r+r /*handy─dandy variables. */
do i=floor(-r ) to ceil(r ); x= i + .5; xx= x**2; $=
do j=floor(-r2) to ceil(r2); y= j * .5 + .5; yy= y**2; z= xx+yy
if z<=rr then do /*is point within sphere ? */
parse value norm(x y sqrt(rr - xx - yy) ) with v1 v2 v3
dot= min(0, s1*v1 + s2*v2 + s3*v3) /*the dot product of above.*/
b= -dot**k + ambient /*calculate the brightness.*/
if b<=0 then brite= shadeLen
else brite= max(0, (1-b) * shadeLen) % 1
$= $ || substr(shading, brite + 1, 1)
end /* [↑] build display line.*/
else $= $' ' /*append a blank to line. */
end /*j*/ /*[↓] strip trailing blanks*/
say strip($, 'T') /*show a line of the sphere*/
end /*i*/ /* [↑] display the sphere.*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d= digits(); numeric digits; h= d+6
numeric form; m.=9; parse value format(x,2,1,,0) 'E0' with g "E" _ .; g= g*.5'e'_%2
do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; return g
- output when using the default input and executed on an ASCII machine:
(Shown at 1/2 size.)
eeeeeeeeee@@@@@@@
eoooooooooooooooeeeee@@@@@@@░
oo°°°!!!!!!!!°°°°°°ooooeeeee@@@@@@@░░
o°°!!!:::::::::!!!!!°°°°°ooooeeee@@@@@@@░░░
o°!!::::·········:::::!!!!°°°ooooeeeee@@@@@@@░░░░
o°!:::················::::!!!°°°°oooeeeee@@@@@@@░░░░░
o°!::····················::::!!!°°°°oooeeeee@@@@@@@░░░░░░
o°!::·······················:::!!!!°°°ooooeeee@@@@@@@@░░░░░░░
o°!::·························:::!!!°°°ooooeeeee@@@@@@@░░░░░░░░
o°!:···························:::!!!°°°°oooeeeee@@@@@@@@░░░░░░░░
o°!::··························::::!!!°°°ooooeeeee@@@@@@@@░░░░░░░░░
o°!::···························:::!!!!°°°ooooeeeee@@@@@@@@░░░░░░░░░░
o°!!::··························::::!!!°°°°ooooeeeee@@@@@@@@░░░░░░░░░░░
eo°!!::·························::::!!!°°°°ooooeeeee@@@@@@@@@░░░░░░░░░░░░
oo°!!::························::::!!!°°°°ooooeeeeee@@@@@@@@░░░░░░░░░░░░░
eoo°!!:::·····················::::!!!!°°°°oooooeeeee@@@@@@@@@░░░░░░░░░░░░░░
eoo°°!!:::·················:::::!!!!!°°°°ooooeeeeee@@@@@@@@@░░░░░░░░░░░░░░░
eoo°°!!!:::::··········:::::::!!!!!°°°°oooooeeeeee@@@@@@@@@@░░░░░░░░░░░░░░░
eeoo°°°!!!:::::::::::::::::!!!!!!°°°°°oooooeeeeee@@@@@@@@@@░░░░░░░░░░░░░░░░
eeooo°°°!!!!!!!:::::::!!!!!!!!°°°°°°oooooeeeeee@@@@@@@@@@@░░░░░░░░░░░░░░░░░
@eeooo°°°°°!!!!!!!!!!!!!!!°°°°°°°ooooooeeeeeee@@@@@@@@@@@░░░░░░░░░░░░░░░░░░
@@eeeoooo°°°°°°°°°°°°°°°°°°°°°oooooooeeeeeee@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░
@@@eeeoooooo°°°°°°°°°°°°°oooooooooeeeeeeee@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░
@@@eeeeeooooooooooooooooooooooeeeeeeeee@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░
@@@@@eeeeeeeooooooooooooeeeeeeeeeeee@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░
@@@@@@eeeeeeeeeeeeeeeeeeeeeeeee@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░
@@@@@@@@@eeeeeeeeeeeeeeeee@@@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░░
░@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░@@@@@@@@@@@@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░@@@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░
::···:::!!!°o
··············::!!°oo
··················::!!°°ooe
·····················::!!°°ooee
·······················::!!°°ooee
························::!!°°oooee
·························::!!°°oooeee
:························::!!!°°oooeeee
························::!!!°°ooooeeee
:······················::!!!°°°oooeeeee
:····················:::!!!°°°oooeeeeee
!:·················:::!!!°°°°oooeeeeeee
°!:::···········::::!!!!°°°ooooeeeeeeee
°!!!:::::::::::!!!!!°°°°oooooeeeeeeee
o°°!!!!!!!!!!!!!°°°°°oooooeeeeeeeee
oo°°°°°°°°°°°°°°ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
Ruby
Shoes comes with this sample program.
Shoes.app :width => 500, :height => 500, :resizable => false do
image 400, 470, :top => 30, :left => 50 do
nostroke
fill "#127"
image :top => 230, :left => 0 do
oval 70, 130, 260, 40
blur 30
end
oval 10, 10, 380, 380
image :top => 0, :left => 0 do
fill "#46D"
oval 30, 30, 338, 338
blur 10
end
fill gradient(rgb(1.0, 1.0, 1.0, 0.7), rgb(1.0, 1.0, 1.0, 0.0))
oval 80, 14, 240, 176
image :top => 0, :left => 0 do
fill "#79F"
oval 134, 134, 130, 130
blur 40
end
image :top => 150, :left => 40, :width => 320, :height => 260 do
fill gradient(rgb(0.7, 0.9, 1.0, 0.0), rgb(0.7, 0.9, 1.0, 0.6))
oval 60, 60, 200, 136
blur 20
end
end
end
Rust
// [dependencies]
// image = "0.23"
use image::{GrayImage, Luma};
type Vector = [f64; 3];
fn normalize(v: &mut Vector) {
let inv_len = 1.0/dot_product(v, v).sqrt();
v[0] *= inv_len;
v[1] *= inv_len;
v[2] *= inv_len;
}
fn dot_product(v1: &Vector, v2: &Vector) -> f64 {
v1.iter().zip(v2.iter()).map(|(x, y)| *x * *y).sum()
}
fn draw_sphere(radius: u32, k: f64, ambient: f64, dir: &Vector) -> GrayImage {
let width = radius * 4;
let height = radius * 3;
let mut image = GrayImage::new(width, height);
let mut vec = [0.0; 3];
let diameter = radius * 2;
let r = radius as f64;
let xoffset = (width - diameter)/2;
let yoffset = (height - diameter)/2;
for i in 0..diameter {
let x = i as f64 - r;
for j in 0..diameter {
let y = j as f64 - r;
let z = r * r - x * x - y * y;
if z >= 0.0 {
vec[0] = x;
vec[1] = y;
vec[2] = z.sqrt();
normalize(&mut vec);
let mut s = dot_product(&dir, &vec);
if s < 0.0 {
s = 0.0;
}
let mut lum = 255.0 * (s.powf(k) + ambient)/(1.0 + ambient);
if lum < 0.0 {
lum = 0.0;
} else if lum > 255.0 {
lum = 255.0;
}
image.put_pixel(i + xoffset, j + yoffset, Luma([lum as u8]));
}
}
}
image
}
fn main() {
let mut dir = [-30.0, -30.0, 50.0];
normalize(&mut dir);
match draw_sphere(200, 1.5, 0.2, &dir).save("sphere.png") {
Ok(()) => {}
Err(error) => eprintln!("{}", error),
}
}
- Output:
Scala
object Sphere extends App {
private val (shades, light) = (Seq('.', ':', '!', '*', 'o', 'e', '&', '#', '%', '@'), Array(30d, 30d, -50d))
private def drawSphere(r: Double, k: Double, ambient: Double): Unit = {
def dot(x: Array[Double], y: Array[Double]) = {
val d = x.head * y.head + x(1) * y(1) + x.last * y.last
if (d < 0) -d else 0D
}
for (i <- math.floor(-r).toInt to math.ceil(r).toInt; x = i + .5)
println(
(for (j <- math.floor(-2 * r).toInt to math.ceil(2 * r).toInt; y = j / 2.0 + .5)
yield if (x * x + y * y <= r * r) {
def intensity(vec: Array[Double]) = {
val b = math.pow(dot(light, vec), k) + ambient
if (b <= 0) shades.length - 2
else math.max((1 - b) * (shades.length - 1), 0).toInt
}
shades(intensity(normalize(Array(x, y, scala.math.sqrt(r * r - x * x - y * y)))))
} else ' ').mkString)
}
private def normalize(v: Array[Double]): Array[Double] = {
val len = math.sqrt(v.head * v.head + v(1) * v(1) + v.last * v.last)
v.map(_ / len)
}
normalize(light).copyToArray(light)
drawSphere(20, 4, .1)
drawSphere(10, 2, .4)
}
- Output:
See it in running in your browser by ScalaFiddle (JavaScript) or by Scastie (JVM).
Sidef
Produces a PGM image.
func normalize (vec) { vec »/» (vec »*« vec -> sum.sqrt) }
func dot (x, y) { -(x »*« y -> sum) `max` 0 }
var x = var y = 255
x += 1 if x.is_even # must be odd
var light = normalize([ 3, 2, -5 ])
var depth = 255
func draw_sphere(rad, k, ambient) {
var pixels = []
var r2 = (rad * rad)
var range = (-rad .. rad)
for x,y in (range ~X range) {
if